tomleslie

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10 years, 142 days

MaplePrimes Activity


These are replies submitted by tomleslie

I thiught my response in the following thread

https://www.mapleprimes.com/questions/229996-The-Problem-With-Updating-The-Physics-Package

fixed your problem?

Did it, or didn't it?

I did warn you in that thread, every time you try to update the Physics Package, you are probably going to have to repeat the  process I outlined. And all because the MapleSoft update process is completely incapable of making a couple of files "appear" in the correct places

Still, it does give one a lot of confidence about MapleSoft's ability to produce reliable software - NOT

because, I don't have anything so OLD.

Just a suggestion - the problem may be with the and() function, so I might be tempted to try something involving a simple algebraic expression, rather than a boolean - such as

event1 := [ gln[1]^2+gln[2]^2, halt]]

 

@janhardo 

I seem to have fixed most of the problems in your original question, and the techniques I have used are generally applicable to any problem.

But now you come up with a new issue - that it is "not a general procedure yet and making one could be complicated?"

Actually I disagree - it is trivial to convert my original worksheet into a more "general" procedure, but a lot depends on exactly what kind of input data you want to handle.

Consider the attached

  restart;
  with(plots):
  doPlot:= proc( A )
                 display
                 ( [ seq
                     ( seq
                       ( plot3d
                         ( A[i,j],
                           x=i-1..i,
                           y=j-1..j,
                           shading=zhue,
                           style=surface,
                           axes=normal,
                           view=[ 0..op([2, 1, 2], A),
                                  0..op([2, 2, 2], A),
                                  min(0, A[..,2] )..max(A[..,2])
                                ]
                         ),
                         i=1..op([2,1, 2], A)
                       ),
                       j=1..2
                     )
                   ],
                   scaling=constrained,
                   size=[1000, 1000]
                 );
          end proc:
  T1:=Array( [ [ 0.5, -1  ],
               [ 1,    2  ]
             ]
           ):
  T2:=Array( [ [ 0.5, -1  ],
               [ 1,    2  ],
               [ 1.5,  1  ],
               [ 1.75, 2  ],
               [ 2,    2.5]
            ]
          ):
  doPlot(T1);
  doPlot(T2);

 

 

 

Download arrplot3.mw

 

@jalal 

the attached perhaps?

  restart;
  with(plots): with(plottools): with(ColorTools): with(combinat):

#
# Number of terms in the fibonacci sequence. Ajust
# as required
#
  N:=24:
#
# A couple of utilities
#
  g:= k-> round~( convert( op(1, a[k])[-1,..], list)):
  h:= k-> round~( convert( op(1, a[k])[1,..], list)):
#
# Initialise the first arc and rectangle
#
  a[1]:= arc( [0,0], fibonacci(1),0..Pi/2):
  r[1]:= rectangle( g(1), h(1)):

#
# Loop through all subsequent arc sections and
# rectangles
#
  for j from 2 by 1 to N do
      fj:=fibonacci(j):
    #
    # Generate the arc section
    #
      a[j]:= arc
             ( [ g(j-1)[1]+cos((j+1)*Pi/2)*fj,
                 g(j-1)[2]+sin((j+1)*Pi/2)*fj
               ],             
               fj,
               (j-1)*Pi/2..j*Pi/2
             );
    #
    # and the corresponding rectangle
    #
      r[j]:= rectangle
             ( g(j),
               h(j),
               color=Color( [ seq( rand()/10^12, k=1..3 ) ] )
             );
  od:

#
# Animate both the arc and the rectangles of the spiral
#
  display
  ( [ seq
      ( display
        ( [ seq( [a[j],r[j]][], j=1..i)],
           caption=typeset( "Fibonacci number is %1",
                            fibonacci(i)
                          ),
           captionfont=[times, bold, 24]
        ),
        i=1..N
      )
    ],
    titlefont=[times, bold, 24],
    scaling=constrained,
    axes=none,
    insequence=true,
    size=[1200,1200]
  );

 

 


 

Download fibSpiral2.mw

@CR 

which at least seems to make both data sets the same. I'd upload an example, but when I try this site is giving me a "secure server error"

 

@Jean-Michel Collard 

Next time you update your Physics - you may have to play a similar game - unless Maplesoft actually get their act together!

@ogunmiloro 

  1. In your worksheet, you imply that the lists aca 'times' and 'C__f'' contain experimetal data. So why are these lists of different lengths? In the optimisation process you are only using the first ~20 entries in the C__f list, ie the values 1, 1, [1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 8]. Is this intentional!!!!!
  2. Let us consider the first entries in these two lists, from the 'times' list we get 5 and from the C__f list we get 1. This suggest that for small values of the independent variable 'T' yoiu expect small (ie~1) values of the independent varaible C(T). However your ODE system contains the initial condition C(0)=160000.
  3. In other words you are taking the values of the independent variable given by the list [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100], with corresponding values of the dependent variable [1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 8] and you want to 'fit' these to a function C(T) which has the condition C(0)=160000. Does this sound even remotely sensible to you?
  4. In the attached I have used the (free) DirectSearch() package to investigate this issue further. You (probably) will not have the DirectSearch package installed - so you will not be able to execute this worksheet. This worksheet demonstrates two things
    1. with the initial values of the parameters l, m, n, q, r, u, v, sigma, iota, nu, phi, upsilon, delta, g which you supply, the fit  is absoutely terrible, which can be seen in the attached both from the residual error and by comparing graphs of the "experimental data" and the ODE solution for C(T)
    2. with the optimised values of all the parameters returned by DirectSearch(), the value of the residual error is greatly reduced - but the overall fit is still terrible, as can be seen from the graphs.

I think you seriously have to address the issue of the mismatch between the initial condition for the ODE system, ie C(0)=160000, and the values of your 'experimental data' for low values of T

Bearing in mnd all of the above - I would say that what the attached produces is pretty much rubbish - although it does 'execute' provided you have the DirectSearch package installed

restart; with(plots); with(Optimization); with(Statistics)

A := 0.346e-1; mu := 0.491e-1
Parameterizing (with respect to l, m, n, rho, k, q, r, u, v, sigma, iota, nu, phi, upsilon, w, x, delta, g) the numerical solution of the model deq
      #Calculating the sum of the square of the errors between the model predictions and experimental data
     #Minimizing the sum of the square of the errors to find the best fit values of " l, m, n ,rho, k, q, r, u , v , sigma, iota, nu, phi,upsilon, w, x, delta, g."

0.346e-1

 

0.491e-1

(1)

times := [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100]

[5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100]

(2)

C__f := [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 8, 12, 12, 22, 30, 40, 44, 51, 65, 70, 97, 111, 131, 135, 174, 184, 210, 214, 232, 238, 254, 276, 285, 305, 318, 323, 343, 373, 407, 442, 493, 542, 627, 665, 782, 873, 981, 1095, 1182, 1273, 1337, 1532, 1728, 1932, 2170, 2388, 2558, 2802, 2950, 3145, 3526, 3912, 4151, 4399, 4641, 4787, 4971, 5162, 5445, 5621, 5959, 6175, 6401, 6677, 7016, 7261, 7526, 7839, 8068, 8344, 8733, 8915, 9302, 9855, 10162, 10819, 11166, 11516, 11844, 12233, 12486, 12801, 13464, 13873, 14554, 15181, 15682, 16085, 16658, 17148, 17735]

DE1 := diff(B(T), T) = A-l*B(T)*C(T)/(1+sigma*C(T))-nu*m*B(T)*P(T)/(1+iota*P(T))-mu*B(T)-n*B(T)*E(T)/(E(T)+g); DE2 := diff(C(T), T) = l*B(T)*C(T)/(1+sigma*C(T))-q*C(T)-r*C(T)-phi; DE3 := diff(P(T), T) = nu*m*B(T)*P(T)/(1+iota*P(T))-u*P(T)-v*P(T)-upsilon; DE4 := diff(E(T), T) = phi*C(T)+upsilon*P(T)-delta*E(T); DE5 := diff(F(T), T) = q*C(T)+u*P(T)-mu*F(T); ics := B(0) = 19000, C(0) = 160000, P(0) = 17000, E(0) = 10000, F(0) = 15500

res := dsolve({DE1, DE2, DE3, DE4, DE5, ics}, parameters = [l, m, n, q, r, u, v, sigma, iota, nu, phi, upsilon, delta, g], numeric)

proc (x_rkf45) local _res, _dat, _vars, _solnproc, _xout, _ndsol, _pars, _n, _i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; if 1 < nargs then error "invalid input: too many arguments" end if; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then _xout := evalf[_EnvDSNumericSaveDigits](x_rkf45) else _xout := evalf(x_rkf45) end if; _dat := Array(1..4, {(1) = proc (_xin) local _xout, _dtbl, _dat, _vmap, _x0, _y0, _val, _dig, _n, _ne, _nd, _nv, _pars, _ini, _par, _i, _j, _k, _src; option `Copyright (c) 2002 by Waterloo Maple Inc. All rights reserved.`; table( [( "complex" ) = false ] ) _xout := _xin; _pars := [l = l, m = m, n = n, q = q, r = r, u = u, v = v, sigma = sigma, iota = iota, nu = nu, phi = phi, upsilon = upsilon, delta = delta, g = g]; _dtbl := array( 1 .. 4, [( 1 ) = (array( 1 .. 26, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..63, {(1) = 5, (2) = 5, (3) = 0, (4) = 0, (5) = 14, (6) = 0, (7) = 0, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 0, (19) = 30000, (20) = 0, (21) = 0, (22) = 1, (23) = 4, (24) = 0, (25) = 1, (26) = 15, (27) = 1, (28) = 0, (29) = 1, (30) = 3, (31) = 3, (32) = 0, (33) = 1, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 1, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 50, (51) = 1, (52) = 0, (53) = 0, (54) = 0, (55) = 0, (56) = 0, (57) = 0, (58) = 0, (59) = 10000, (60) = 0, (61) = 1000, (62) = 0, (63) = 0}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = .0, (2) = 0.10e-5, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = .0, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 6 ) = (Array(1..19, {(1) = 19000., (2) = 160000., (3) = 10000., (4) = 15500., (5) = 17000., (6) = Float(undefined), (7) = Float(undefined), (8) = Float(undefined), (9) = Float(undefined), (10) = Float(undefined), (11) = Float(undefined), (12) = Float(undefined), (13) = Float(undefined), (14) = Float(undefined), (15) = Float(undefined), (16) = Float(undefined), (17) = Float(undefined), (18) = Float(undefined), (19) = Float(undefined)})), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..5, {(1) = .1, (2) = .1, (3) = .1, (4) = .1, (5) = .1}, datatype = float[8], order = C_order), Array(1..5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8], order = C_order), Array(1..5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8], order = C_order), Array(1..5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8], order = C_order), Array(1..5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8], order = C_order), Array(1..5, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0}, datatype = float[8], order = C_order), Array(1..5, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0}, datatype = float[8], order = C_order), Array(1..5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8], order = C_order), Array(1..5, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0}, datatype = float[8], order = C_order), Array(1..5, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0}, datatype = float[8], order = C_order), Array(1..5, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0}, datatype = integer[8]), Array(1..19, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0}, datatype = float[8], order = C_order), Array(1..19, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0}, datatype = float[8], order = C_order), Array(1..19, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0}, datatype = float[8], order = C_order), Array(1..19, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0}, datatype = float[8], order = C_order), Array(1..5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8], order = C_order), Array(1..10, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0}, datatype = float[8], order = C_order), Array(1..5, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0}, datatype = integer[8])]), ( 8 ) = ([Array(1..19, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0}, datatype = float[8], order = C_order), Array(1..19, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0}, datatype = float[8], order = C_order), Array(1..5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 0) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 0) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 0) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (5, 0) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (6, 0) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = B(T), Y[2] = C(T), Y[3] = E(T), Y[4] = F(T), Y[5] = P(T)]`; YP[1] := 0.346e-1-Y[6]*Y[1]*Y[2]/(Y[2]*Y[13]+1)-Y[15]*Y[7]*Y[1]*Y[5]/(Y[5]*Y[14]+1)-0.491e-1*Y[1]-Y[8]*Y[1]*Y[3]/(Y[3]+Y[19]); YP[2] := Y[6]*Y[1]*Y[2]/(Y[2]*Y[13]+1)-Y[9]*Y[2]-Y[10]*Y[2]-Y[16]; YP[3] := Y[2]*Y[16]-Y[3]*Y[18]+Y[5]*Y[17]; YP[4] := Y[9]*Y[2]+Y[11]*Y[5]-0.491e-1*Y[4]; YP[5] := Y[15]*Y[7]*Y[1]*Y[5]/(Y[5]*Y[14]+1)-Y[11]*Y[5]-Y[12]*Y[5]-Y[17]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 18 ) = ([]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = B(T), Y[2] = C(T), Y[3] = E(T), Y[4] = F(T), Y[5] = P(T)]`; YP[1] := 0.346e-1-Y[6]*Y[1]*Y[2]/(Y[2]*Y[13]+1)-Y[15]*Y[7]*Y[1]*Y[5]/(Y[5]*Y[14]+1)-0.491e-1*Y[1]-Y[8]*Y[1]*Y[3]/(Y[3]+Y[19]); YP[2] := Y[6]*Y[1]*Y[2]/(Y[2]*Y[13]+1)-Y[9]*Y[2]-Y[10]*Y[2]-Y[16]; YP[3] := Y[2]*Y[16]-Y[3]*Y[18]+Y[5]*Y[17]; YP[4] := Y[9]*Y[2]+Y[11]*Y[5]-0.491e-1*Y[4]; YP[5] := Y[15]*Y[7]*Y[1]*Y[5]/(Y[5]*Y[14]+1)-Y[11]*Y[5]-Y[12]*Y[5]-Y[17]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0)  ] ))  ] ); _y0 := Array(0..19, {(1) = 0., (2) = 19000., (3) = 160000., (4) = 10000., (5) = 15500., (6) = 17000., (7) = undefined, (8) = undefined, (9) = undefined, (10) = undefined, (11) = undefined, (12) = undefined, (13) = undefined, (14) = undefined, (15) = undefined, (16) = undefined, (17) = undefined, (18) = undefined, (19) = undefined}); _vmap := array( 1 .. 5, [( 1 ) = (1), ( 2 ) = (2), ( 3 ) = (3), ( 4 ) = (4), ( 5 ) = (5)  ] ); _x0 := _dtbl[1][5][5]; _n := _dtbl[1][4][1]; _ne := _dtbl[1][4][3]; _nd := _dtbl[1][4][4]; _nv := _dtbl[1][4][16]; if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then if _Env_smart_dsolve_numeric = true or _dtbl[1][4][10] = 1 then if _xout = "left" then if type(_dtbl[2], 'table') then return _dtbl[2][5][1] end if elif _xout = "right" then if type(_dtbl[3], 'table') then return _dtbl[3][5][1] end if end if end if; return _dtbl[1][5][5] elif _xout = "method" then return _dtbl[1][15] elif _xout = "storage" then return evalb(_dtbl[1][4][10] = 1) elif _xout = "leftdata" then if not type(_dtbl[2], 'array') then return NULL else return eval(_dtbl[2]) end if elif _xout = "rightdata" then if not type(_dtbl[3], 'array') then return NULL else return eval(_dtbl[3]) end if elif _xout = "enginedata" then return eval(_dtbl[1]) elif _xout = "enginereset" then _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); return NULL elif _xout = "initial" then return procname(_y0[0]) elif _xout = "laxtol" then return _dtbl[`if`(member(_dtbl[4], {2, 3}), _dtbl[4], 1)][5][18] elif _xout = "numfun" then return `if`(member(_dtbl[4], {2, 3}), _dtbl[_dtbl[4]][4][18], 0) elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return procname(_y0[0]), [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _dtbl[4] <> 2 and _dtbl[4] <> 3 or _x0-_dtbl[_dtbl[4]][5][1] = 0. then error "no information is available on last computed point" else _xout := _dtbl[_dtbl[4]][5][1] end if elif _xout = "function" then if _dtbl[1][4][33]-2. = 0 then return eval(_dtbl[1][10], 1) else return eval(_dtbl[1][10][1], 1) end if elif _xout = "map" then return copy(_vmap) elif type(_xin, `=`) and type(rhs(_xin), 'list') and member(lhs(_xin), {"initial", "parameters", "initial_and_parameters"}) then _ini, _par := [], []; if lhs(_xin) = "initial" then _ini := rhs(_xin) elif lhs(_xin) = "parameters" then _par := rhs(_xin) elif select(type, rhs(_xin), `=`) <> [] then _par, _ini := selectremove(type, rhs(_xin), `=`) elif nops(rhs(_xin)) < nops(_pars)+1 then error "insufficient data for specification of initial and parameters" else _par := rhs(_xin)[-nops(_pars) .. -1]; _ini := rhs(_xin)[1 .. -nops(_pars)-1] end if; _xout := lhs(_xout); _i := false; if _par <> [] then _i := `dsolve/numeric/process_parameters`(_n, _pars, _par, _y0) end if; if _ini <> [] then _i := `dsolve/numeric/process_initial`(_n-_ne, _ini, _y0, _pars, _vmap) or _i end if; if _i then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars); if _Env_smart_dsolve_numeric = true and type(_y0[0], 'numeric') and _dtbl[1][4][10] <> 1 then procname("right") := _y0[0]; procname("left") := _y0[0] end if end if; if _xout = "initial" then return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)] elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] else return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)], [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] end if elif _xin = "eventstop" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then return 0 end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 <= _dtbl[5-_i][4][9] then _i := 5-_i; _dtbl[4] := _i; _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) elif 100 <= _dtbl[_i][4][9] then _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) else return 0 end if elif _xin = "eventstatus" then if _nv = 0 then error "this solution has no events" end if; _i := [selectremove(proc (a) options operator, arrow; _dtbl[1][3][1][a, 7] = 1 end proc, {seq(_j, _j = 1 .. round(_dtbl[1][3][1][_nv+1, 1]))})]; return ':-enabled' = _i[1], ':-disabled' = _i[2] elif _xin = "eventclear" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then error "no events to clear" end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 < _dtbl[5-_i][4][9] then _dtbl[4] := 5-_i; _i := 5-_i end if; if _dtbl[_i][4][9] < 100 then error "no events to clear" elif _nv < _dtbl[_i][4][9]-100 then error "event error condition cannot be cleared" else _j := _dtbl[_i][4][9]-100; if irem(round(_dtbl[_i][3][1][_j, 4]), 2) = 1 then error "retriggerable events cannot be cleared" end if; _j := round(_dtbl[_i][3][1][_j, 1]); for _k to _nv do if _dtbl[_i][3][1][_k, 1] = _j then if _dtbl[_i][3][1][_k, 2] = 3 then error "range events cannot be cleared" end if; _dtbl[_i][3][1][_k, 8] := _dtbl[_i][3][1][_nv+1, 8] end if end do; _dtbl[_i][4][17] := 0; _dtbl[_i][4][9] := 0; if _dtbl[1][4][10] = 1 then if _i = 2 then try procname(procname("left")) catch:  end try else try procname(procname("right")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and member(lhs(_xin), {"eventdisable", "eventenable"}) then if _nv = 0 then error "this solution has no events" end if; if type(rhs(_xin), {('list')('posint'), ('set')('posint')}) then _i := {op(rhs(_xin))} elif type(rhs(_xin), 'posint') then _i := {rhs(_xin)} else error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; if select(proc (a) options operator, arrow; _nv < a end proc, _i) <> {} then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _k := {}; for _j to _nv do if member(round(_dtbl[1][3][1][_j, 1]), _i) then _k := `union`(_k, {_j}) end if end do; _i := _k; if lhs(_xin) = "eventdisable" then _dtbl[4] := 0; _j := [evalb(assigned(_dtbl[2]) and member(_dtbl[2][4][17], _i)), evalb(assigned(_dtbl[3]) and member(_dtbl[3][4][17], _i))]; for _k in _i do _dtbl[1][3][1][_k, 7] := 0; if assigned(_dtbl[2]) then _dtbl[2][3][1][_k, 7] := 0 end if; if assigned(_dtbl[3]) then _dtbl[3][3][1][_k, 7] := 0 end if end do; if _j[1] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[2][3][4][_k, 1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to defined init `, _dtbl[2][3][4][_k, 1]); _dtbl[2][3][1][_k, 8] := _dtbl[2][3][4][_k, 1] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to rate hysteresis init `, _dtbl[2][5][24]); _dtbl[2][3][1][_k, 8] := _dtbl[2][5][24] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to initial init `, _x0); _dtbl[2][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to fireinitial init `, _x0-1); _dtbl[2][3][1][_k, 8] := _x0-1 end if end do; _dtbl[2][4][17] := 0; _dtbl[2][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("left")) end if end if; if _j[2] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[3][3][4][_k, 2], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to defined init `, _dtbl[3][3][4][_k, 2]); _dtbl[3][3][1][_k, 8] := _dtbl[3][3][4][_k, 2] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to rate hysteresis init `, _dtbl[3][5][24]); _dtbl[3][3][1][_k, 8] := _dtbl[3][5][24] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to initial init `, _x0); _dtbl[3][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to fireinitial init `, _x0+1); _dtbl[3][3][1][_k, 8] := _x0+1 end if end do; _dtbl[3][4][17] := 0; _dtbl[3][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("right")) end if end if else for _k in _i do _dtbl[1][3][1][_k, 7] := 1 end do; _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); _dtbl[4] := 0; if _dtbl[1][4][10] = 1 then if _x0 <= procname("right") then try procname(procname("right")) catch:  end try end if; if procname("left") <= _x0 then try procname(procname("left")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and lhs(_xin) = "eventfired" then if not type(rhs(_xin), 'list') then error "'eventfired' must be specified as a list" end if; if _nv = 0 then error "this solution has no events" end if; if _dtbl[4] <> 2 and _dtbl[4] <> 3 then error "'direction' must be set prior to calling/setting 'eventfired'" end if; _i := _dtbl[4]; _val := NULL; if not assigned(_EnvEventRetriggerWarned) then _EnvEventRetriggerWarned := false end if; for _k in rhs(_xin) do if type(_k, 'integer') then _src := _k elif type(_k, 'integer' = 'anything') and type(evalf(rhs(_k)), 'numeric') then _k := lhs(_k) = evalf[max(Digits, 18)](rhs(_k)); _src := lhs(_k) else error "'eventfired' entry is not valid: %1", _k end if; if _src < 1 or round(_dtbl[1][3][1][_nv+1, 1]) < _src then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _src := {seq(`if`(_dtbl[1][3][1][_j, 1]-_src = 0., _j, NULL), _j = 1 .. _nv)}; if nops(_src) <> 1 then error "'eventfired' can only be set/queried for root-finding events and time/interval events" end if; _src := _src[1]; if _dtbl[1][3][1][_src, 2] <> 0. and _dtbl[1][3][1][_src, 2]-2. <> 0. then error "'eventfired' can only be set/queried for root-finding events and time/interval events" elif irem(round(_dtbl[1][3][1][_src, 4]), 2) = 1 then if _EnvEventRetriggerWarned = false then WARNING(`'eventfired' has no effect on events that retrigger`) end if; _EnvEventRetriggerWarned := true end if; if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then _val := _val, undefined elif type(_dtbl[_i][3][4][_src, _i-1], 'undefined') or _i = 2 and _dtbl[2][3][1][_src, 8] < _dtbl[2][3][4][_src, 1] or _i = 3 and _dtbl[3][3][4][_src, 2] < _dtbl[3][3][1][_src, 8] then _val := _val, _dtbl[_i][3][1][_src, 8] else _val := _val, _dtbl[_i][3][4][_src, _i-1] end if; if type(_k, `=`) then if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then error "cannot set event code for a rate hysteresis event" end if; userinfo(3, {'events', 'eventreset'}, `manual set event code `, _src, ` to value `, rhs(_k)); _dtbl[_i][3][1][_src, 8] := rhs(_k); _dtbl[_i][3][4][_src, _i-1] := rhs(_k) end if end do; return [_val] elif type(_xin, `=`) and lhs(_xin) = "direction" then if not member(rhs(_xin), {-1, 1, ':-left', ':-right'}) then error "'direction' must be specified as either '1' or 'right' (positive) or '-1' or 'left' (negative)" end if; _src := `if`(_dtbl[4] = 2, -1, `if`(_dtbl[4] = 3, 1, undefined)); _i := `if`(member(rhs(_xin), {1, ':-right'}), 3, 2); _dtbl[4] := _i; _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if; return _src elif _xin = "eventcount" then if _dtbl[1][3][1] = 0 or _dtbl[4] <> 2 and _dtbl[4] <> 3 then return 0 else return round(_dtbl[_dtbl[4]][3][1][_nv+1, 12]) end if else return "procname" end if end if; if _xout = _x0 then return [_x0, seq(evalf(_dtbl[1][6][_vmap[_i]]), _i = 1 .. _n-_ne)] end if; _i := `if`(_x0 <= _xout, 3, 2); if _xin = "last" and 0 < _dtbl[_i][4][9] and _dtbl[_i][4][9] < 100 then _dat := eval(_dtbl[_i], 2); _j := _dat[4][20]; return [_dat[11][_j, 0], seq(_dat[11][_j, _vmap[_i]], _i = 1 .. _n-_ne-_nd), seq(_dat[8][1][_vmap[_i]], _i = _n-_ne-_nd+1 .. _n-_ne)] end if; if not type(_dtbl[_i], 'array') then _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if end if; if _xin <> "last" then if 0 < 0 then if `dsolve/numeric/checkglobals`(op(_dtbl[1][14]), _pars, _n, _y0) then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars, _i) end if end if; if _dtbl[1][4][7] = 0 then error "parameters must be initialized before solution can be computed" end if end if; _dat := eval(_dtbl[_i], 2); _dtbl[4] := _i; try _src := `dsolve/numeric/SC/IVPrun`(_dat, _xout) catch: userinfo(2, `dsolve/debug`, print(`Exception in solnproc:`, [lastexception][2 .. -1])); error  end try; if _dat[17] <> _dtbl[1][17] then _dtbl[1][17] := _dat[17]; _dtbl[1][10] := _dat[10] end if; if _src = 0 and 100 < _dat[4][9] then _val := _dat[3][1][_nv+1, 8] else _val := _dat[11][_dat[4][20], 0] end if; if _src <> 0 or _dat[4][9] <= 0 then _dtbl[1][5][1] := _xout else _dtbl[1][5][1] := _val end if; if _i = 3 and _val < _xout then Rounding := -infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further right of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further right of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further right of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further right of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further right of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further right of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further right of %1", evalf[8](_val) end if elif _i = 2 and _xout < _val then Rounding := infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further left of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further left of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further left of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further left of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further left of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further left of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further left of %1", evalf[8](_val) end if end if; if _EnvInFsolve = true then _dig := _dat[4][26]; if type(_EnvDSNumericSaveDigits, 'posint') then _dat[4][26] := _EnvDSNumericSaveDigits else _dat[4][26] := Digits end if; _Env_dsolve_SC_native := true; if _dat[4][25] = 1 then _i := 1; _dat[4][25] := 2 else _i := _dat[4][25] end if; _val := `dsolve/numeric/SC/IVPval`(_dat, _xout, _src); _dat[4][25] := _i; _dat[4][26] := _dig; [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] else Digits := _dat[4][26]; _val := `dsolve/numeric/SC/IVPval`(eval(_dat, 2), _xout, _src); [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] end if end proc, (2) = Array(0..0, {}), (3) = [T, B(T), C(T), E(T), F(T), P(T)], (4) = [l = l, m = m, n = n, q = q, r = r, u = u, v = v, sigma = sigma, iota = iota, nu = nu, phi = phi, upsilon = upsilon, delta = delta, g = g]}); _vars := _dat[3]; _pars := map(rhs, _dat[4]); _n := nops(_vars)-1; _solnproc := _dat[1]; if not type(_xout, 'numeric') then if member(x_rkf45, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(x_rkf45, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(x_rkf45, ["last", 'last', "initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(x_rkf45, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] end if elif type(_xout, `=`) and member(lhs(_xout), ["initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(lhs(x_rkf45), 'string') = rhs(x_rkf45); if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else error "initial and/or parameter values must be specified in a list" end if; if lhs(_xout) = "initial" then return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["eventdisable", 'eventdisable', "eventenable", 'eventenable', "eventfired", 'eventfired', "direction", 'direction', NULL]) then return _solnproc(convert(lhs(x_rkf45), 'string') = rhs(x_rkf45)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _vars end if; if procname <> unknown then return ('procname')(x_rkf45) else _ndsol := 1; _ndsol := _ndsol; _ndsol := pointto(_dat[2][0]); return ('_ndsol')(x_rkf45) end if end if; try _res := _solnproc(_xout); [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] catch: error  end try end proc

(3)

sse := proc (l, m, n, q, r, u, v, sigma, iota, nu, phi, upsilon, delta, g) local testRes; res(parameters = [l, m, n, q, r, u, v, sigma, iota, nu, phi, upsilon, delta, g]); try testRes := add((C__f[i]-rhs(res(times[i])[3]))^2, i = 1 .. numelems(times)) catch "cannot evaluate the solution": testRes := 1000000000000 end try; return testRes end proc

#
# Use the OP's list of initial parameter values
#
  initVars:=[ l = 0.05, m = 0.02, n = 0.017, q = 0.004,
              r = 0.098710, u = 0.0100, v = 0.08543,
              sigma = 0.0349, iota = 0.0032, nu = 0.0014,
              phi = 0.931, upsilon = 0.0019, delta = 0.01,
              g = 0.3]:
  res( parameters= rhs~(initVars) );
#
# Plot the value of the ODE solution with these
# initial parameters
#
  plots:-odeplot( res, [T,C(T)], T=5..100, axes=boxed);
#
# plot the pairs [times[j], C__f[j]] - ie the OP's
# "experimental" values - for comparison with the
# ODE solution above
#
  plot( [seq( [times[j],C__f[j]], j=1..numelems(times))]);
  sse( rhs~(initVars)[]);

[l = 0.5e-1, m = 0.2e-1, n = 0.17e-1, q = 0.4e-2, r = 0.98710e-1, u = 0.100e-1, v = 0.8543e-1, sigma = 0.349e-1, iota = 0.32e-2, nu = 0.14e-2, phi = .931, upsilon = 0.19e-2, delta = 0.1e-1, g = .3]

 

 

 

HFloat(1.7940613225317665e10)

(4)

#
# Use DirectSearch() to obtain an "optimal" set of parameters
# NB OP *probably* won't be able to do this because (s)he wont
# have the DirectSearch() package installed.
#
  DSOpts:=DirectSearch:-Search( sse,initialpoint = initVars,assume=positive);

[114.99999999995288, _rtable[18446744074610209246], 2055]

(5)

#
# Double-check the error value returned when using the
# "optimised" parameter values found by DirectSearch()
# (Should return the first value in the DSOpts() Array
# - which it does
  sse( entries(DSOpts[2], nolist));
#
# Plot the value of the ODE solution with these
# initial parameters
#
  res(parameters= [entries(DSOpts[2], nolist)]):
  plots:-odeplot( res, [T,C(T)], T=5..100, axes=boxed);

HFloat(114.99999999995288)

 

 

``


 

Download ODEOpt2.mw

 

post "pictures" of code.

They cannot be executed, cannot be debugged and in fact are almost completely useless - and before you ask, no-one on this site is going to read your code and retype it.

After all why should they when you can upload executable, debuggable code by simply using the big green up-arrow in the Mapleprimes toolbar

@Earl 

Obviously I don't know the complexity of the problem you are trying to address, but for reasonably simple circuits, I would have thought that it would be adequate.

Assuming you have Syrup installed, then you can access thethe general Syrup help by typing

?Syrup

at the Maple command prompt.

Since you ask for examples, you can pull up a pagefull of these of these just by typing

?Syrup/Examples

at the Maple command prompt

@DarkMath 

that you re-read the above-referenced table again

@janhardo 

if you could read the response you have already been given - it means that I doin't have to keep restating the blindingly obvious. So when you state

Looking again to the code.

 

I aspected that yv  -values of f  should be stored in a array, but that happened here.

 

yv:=unapply( f, indets(f, 'name')[])~(xv);

 

But there is not Array made for this at forehand , well perhaps it has to do with the  ~ (xv) operator
It depend then from what datacontainer type( source container)  is used by ~(xv) ?

 

In this case it was a Array ,but was it a list then you get probabably a target datacontainer  list?   Precisley whihc part of this question is NOT covered by the comment from my previous post which states

 

#
# In a similar way, this (nameless) function can be
# applied 'elementwise' to every element in a "container"
# - ie a list, an array, vector etc, by using the '~'
# operator. This will return a container of the same type,
# but with updated entries.

 

And if you really want to understand this in detail then you read the help page at

   help(elementwise);

as I previously advised

 

 

@Reshu Gupta 

and in what format - and only you know that.

If Excel is the desired target, then the simplest way is probably to use the ExcelTools:-Export() command. So adding the command

ExcelTools:-Export(M, "C:/Users/TomLeslie/Desktop/test.xlsx") ;

to the bottom of the worksheet I posted previously will export the matrix 'M' to the Excel file "test.xlsx" at the location "C:/Users/TomLeslie/Desktop". The last of these happens to be my default "desktop" folder. You will have to change this location to something appropriate for your installation

@janhardo 

through the command

unapply( f, indets(f, 'name')[])~(..)

with appropriate help pages

#
# Now suppose you have an expression
#
  f:=x^2+2*x+1;

x^2+2*x+1

(1)

#
# indets(f, 'name') returns all of the unevaluated
# names in the expression 'f' as a set. In this example
# the set only containes one entry.
#
  help(indets);
  indets(f, 'name');

{x}

(2)

#
# On this occasion, we don't want this command
# to return a 'set', we just want the 'entries'.
# There are (at least) a couple of ways to do this
#
# So all this part does is to return the 'unknown'
# variable in the original expression 'f'.
#
  help(list);
  op(indets(f, 'name')); #or
  indets(f, 'name')[];

x

 

x

(3)

#
# By using uanpply(f , indets(f, 'name')[]) the
# original supplied expression is converted to an
# appliable (nameless) function, as in
#
  help(unapply);
  unapply( f, indets(f, 'name')[]);

proc (x) options operator, arrow; x^2+2*x+1 end proc

(4)

#
# This (nameless) function can be applied to an
# argument as in
#
  unapply( f, indets(f, 'name')[])(2);
  unapply( f, indets(f, 'name')[])(a+b);

9

 

(a+b)^2+2*a+2*b+1

(5)

#
# In a similar way, this (nameless) function can be
# applied 'elementwise' to every element in a "container"
# - ie a list, an array, vector etc, by using the '~'
# operator. This will return a container of the same type,
# but with updated entries.
#
# So for the list with entries 1,2,3 and check the returned
# type
#
  help(elementwise);
  unapply( f, indets(f, 'name')[])~([1,2,3]);
  whattype(%);

[4, 9, 16]

 

list

(6)

#
# And for the Array( 1,,2, 1..3, [[1,2,3],[4,5,6]]),
# and check the returned
#
  unapply( f, indets(f, 'name')[])~(Array( 1..2, 1..3, [[ 1,2,3],[4,5,6]]));
  whattype(%);

Matrix(2, 3, {(1, 1) = 4, (1, 2) = 9, (1, 3) = 16, (2, 1) = 25, (2, 2) = 36, (2, 3) = 49})

 

Array

(7)

 


 

Download steps.mw

 

@Reshu Gupta 

which contains

  1. an expression for the the sum f[i](x) for i=0..N
  2. a plot of the expression in (1) above for x=0..5
  3. a matrix containing values of x and sum f[i](x) for i=0..N, where x varies from 0..5 in steps of 0.1

see the attached

  restart;

  N := 4:
#
# Change lhs of the assignment from f(x) to F(x)
# to avoid potential conflict arising from using
# the same name in both indexed and unindexed
# contexts
#
# Also changed sum() to add()
#
  F(x) :=  add(p^i*f[i](x), i = 0..N);
#
# Changed dependent variable throughout from f(x)
# to F(x)
#
  HPMEq := (1 - p)*diff(F(x), x $ 3) + p*(diff(F(x), x $ 3) + 1/2*diff(F(x), x, x)*F(x));
#
# Initialise sol as an empty list
#
  sol:=[]:
  for i from 0 to N do
      sol:= [ sol[],
              dsolve
              ( [ eval
                  ( coeff(HPMEq, p, i) = 0,
                    sol
                  ),
                  f[i](0) = 0,
                  D(f[i])(0) = 0,
                  D(f[i])(5) = 1
                ]
              )
            ];
  end do:
  sol;

 

f[0](x)+p*f[1](x)+p^2*f[2](x)+p^3*f[3](x)+p^4*f[4](x)

 

(1-p)*(diff(diff(diff(f[0](x), x), x), x)+p*(diff(diff(diff(f[1](x), x), x), x))+p^2*(diff(diff(diff(f[2](x), x), x), x))+p^3*(diff(diff(diff(f[3](x), x), x), x))+p^4*(diff(diff(diff(f[4](x), x), x), x)))+p*(diff(diff(diff(f[0](x), x), x), x)+p*(diff(diff(diff(f[1](x), x), x), x))+p^2*(diff(diff(diff(f[2](x), x), x), x))+p^3*(diff(diff(diff(f[3](x), x), x), x))+p^4*(diff(diff(diff(f[4](x), x), x), x))+(1/2)*(diff(diff(f[0](x), x), x)+p*(diff(diff(f[1](x), x), x))+p^2*(diff(diff(f[2](x), x), x))+p^3*(diff(diff(f[3](x), x), x))+p^4*(diff(diff(f[4](x), x), x)))*(f[0](x)+p*f[1](x)+p^2*f[2](x)+p^3*f[3](x)+p^4*f[4](x)))

 

[f[0](x) = (1/10)*x^2, f[1](x) = -(1/6000)*x^5+(73/480)*x^2, f[2](x) = (11/20160000)*x^8-(73/144000)*x^5+(18089/80640)*x^2, f[3](x) = -(1/532224000)*x^11+(803/322560000)*x^8-(36553/32256000)*x^5+(2467369/7741440)*x^2, f[4](x) = (9299/1452971520000000)*x^14-(73/6386688000)*x^11+(808291/108380160000)*x^8-(5108363/2322432000)*x^5+(80546766031/185980354560)*x^2]

(1)

#
# Idle curiosity - what do these functions
# look like
#
  plot( [ seq
          ( rhs(sol[j]),
            j=1..N+1
          )
        ],
        x = 0..5,
        legend = [ seq
                   ( lhs(sol[j]),
                     j=1..N+1
                   )
                 ]
      );

 

#
# Expression for the sum of the functions f[i](x)
# for i from 0..N
#
  fsum:= add
         ( rhs(sol[j]),
           j=1..N+1
         );
#
# And what does the plot of the sum of these
# functions look like
#
  plot( fsum,
        x=0..5
      );
#
# And generate a matrix whose columns are the
# independent variable 'x' and sum(f[i](x)) for
# x=0..5 in steps of 0.1
#
  interface(rtablesize=60):
  M:= Matrix( [ seq
                ( [ i, eval
                       ( add
                         ( rhs(sol[j]),
                           j=1..N+1
                         ),
                         x=i
                       )
                  ],
                  i=0..5, 0.1
                )
              ]
            );
  interface(rtablesize=10):

fsum := (45684823931/37196070912)*x^2-(1860919/464486400)*x^5+(227447/21676032000)*x^8-(17/1277337600)*x^11+(9299/1452971520000000)*x^14

 

 

Matrix(%id = 18446744074536222102)

(2)

 

 

Download odeSols2.mw

@acer 

Funny how often version numbers appear after I complain that they did not exist

Now I can't debug anything in Maple 11 ( released in 2007 ) because I only have the last seven Maple versions (going back to Maple 18 released in 2014). So the only thing I can suggest is to "break down" the offending command into "simple" steps, and see which one fails.

See the highlighted-green execution group in the attached -and report at which stage does it throw an error message in Maple 11. This worksheet (like the one I originally posted) works perfectly in all Maple version from Maple 18 onwards

  restart;
#
# Assorted parameters
#
  T:= 0.1: beta:= 0.6: k:= 3.5:
  A1:= (2*k-1)/(2*k-3):
  A2:= 8*sqrt(2/Pi)*(beta-1)*k*GAMMA(k)/(3*GAMMA(k-0.5)*(2*k-3)**(3/2)):
  A3:= (4*k**2-1)/(2*(2*k-3)**2):
  M1:= 0.1+sqrt(T+(1/A1)):
#
# define ODES and ICs
#
  odes:= diff(U1(x),x)=-diff(phi(x),x)/(U1(x)-T/U1(x)),
         diff(phi(x),x$2)=(1+A1*phi(x)+A2*phi(x)**(3/2)+A3*phi(x)**2)-(M1/U1(x)):
  bcs:= U1(0)=M1, phi(0)=0, D(phi)(0)=0.001:
#
# Solution and plots
#
  sol:= dsolve( [odes, bcs], numeric):
  plots:-odeplot( sol,
                  [ [x, U1(x)],
                    [x, phi(x)],
                    [x, diff(phi(x),x)]
                  ],
                  x=0..20,
                  color= [red ,blue, green]
                );

 

#
# Some tests OP should apply
# What does sol(1) return?
# It should return a list of the values of x (=1)
# U1(x), phi(x) and diff(phi(x),x), all evaluated at x=1
#
  sol(1);
#
# so sol(1)[1..2] should return the first two elements of
# the above list, as in
#
  sol(1)[1..2];
#
# And rhs~( sol(1)[1..2]) ought to return the right hand
# side of the expression in the above list, as in
#
  rhs~( sol(1)[1..2]);
#
# And all the seq() command does, is the above calculation
# for values of x from 0..20, as in
#
  seq( rhs~(sol(j)[1..2]), j=0..20);
#
# And the Matrix() wrapper on this command inserts the data
# into a Matrix wher the firsdt row has been explicitly inserted
# as in x U1(x)
#
  Matrix( [ [ x, U1(x)],
                  seq( rhs~(sol(j)[1..2]), j=0..20)
                ]
              );

[x = 1., U1(x) = .974388249766323, phi(x) = 0.105283221637071e-2, diff(phi(x), x) = 0.115886642863348e-2]

 

[x = 1., U1(x) = .974388249766323]

 

[1., .974388249766323]

 

[0., .975595035800000], [1., .974388249766323], [2., .972803454731538], [3., .970376033430992], [4., .966438414822947], [5., .959991784836733], [6., .949578265984448], [7., .933233907171832], [8., .908762259662163], [9., .874925831097515], [10., .834645490079363], [11., .800094186054956], [12., .790956031097270], [13., .814033485232378], [14., .853460668257642], [15., .891614294714236], [16., .921149911904074], [17., .941628092024671], [18., .954973968794679], [19., .963349571761450], [20., .968492424099562]

 

Matrix(%id = 18446744074330314982)

(1)

#
# Generate the values of x and U1(x) for
# x=0..20 in unit steps
#
  interface(rtablesize=25):
  res:= Matrix( [ [ x, U1(x)],
                  seq( rhs~(sol(j)[1..2]), j=0..20)
                ]
              );
  interface(rtablesize=10):
#
# Now you could use Maple's export() command
# to output the Matrix 'res' in any number of
# different formats - dependin on which format
# the target application understands
#
# But why bother?
#
# After what kind of data processing is available
# is available in the target application, which
# isn't available in Maple?
#
# If I had to guess-the answer would be none at all
#

Matrix(22, 2, {(1, 1) = x, (1, 2) = U1(x), (2, 1) = 0., (2, 2) = .9755950358000001, (3, 1) = 1., (3, 2) = .9743882497663228, (4, 1) = 2., (4, 2) = .9728034547315375, (5, 1) = 3., (5, 2) = .9703760334309917, (6, 1) = 4., (6, 2) = .9664384148229473, (7, 1) = 5., (7, 2) = .9599917848367329, (8, 1) = 6., (8, 2) = .9495782659844485, (9, 1) = 7., (9, 2) = .9332339071718317, (10, 1) = 8., (10, 2) = .9087622596621625, (11, 1) = 9., (11, 2) = .8749258310975149, (12, 1) = 10., (12, 2) = .8346454900793634, (13, 1) = 11., (13, 2) = .8000941860549555, (14, 1) = 12., (14, 2) = .7909560310972703, (15, 1) = 13., (15, 2) = .8140334852323781, (16, 1) = 14., (16, 2) = .8534606682576422, (17, 1) = 15., (17, 2) = .8916142947142357, (18, 1) = 16., (18, 2) = .9211499119040738, (19, 1) = 17., (19, 2) = .941628092024671, (20, 1) = 18., (20, 2) = .9549739687946793, (21, 1) = 19., (21, 2) = .9633495717614502, (22, 1) = 20., (22, 2) = .9684924240995624})

(2)

  restart;
#
# Convert the whole of the above to a procedure
# will accept any values of T, beta, k amd return
# the desired plot
#
  getODESol:= proc( T, beta, k)
                    local A1:= (2*k-1)/(2*k-3),
                          A2:= 8*sqrt(2/Pi)*(beta-1)*k*GAMMA(k)/(3*GAMMA(k-0.5)*(2*k-3)**(3/2)),
                          A3:= (4*k**2-1)/(2*(2*k-3)**2),
                          M1:= 0.1+sqrt(T+(1/A1)),
                        #
                        # define ODES and ICs
                        #
                          odes:= [ diff(U1(x),x)=-diff(phi(x),x)/(U1(x)-T/U1(x)),
                                   diff(phi(x),x$2)=(1+A1*phi(x)+A2*phi(x)**(3/2)+A3*phi(x)**2)-(M1/U1(x))
                                 ],
                          bcs:= [ U1(0)=M1, phi(0)=0, D(phi)(0)=0.001],
                        #
                        # Solution and plots
                        #
                          sol:= dsolve( [odes[], bcs[]], numeric):
                    return plots:-odeplot( sol,
                                           [ [x, U1(x)],
                                             [x, phi(x)],
                                             [x, diff(phi(x),x)]
                                           ],
                                           x=0..20,
                                           color= [red, blue, green]
                                         );
               end proc:
#
# Now plot all sorts of combinations - after all who
# knows what the OP wants/needs
#
  plots:-display( [seq( getODESol( j, 0.6, 3.5), j=0.1..0.5,0.1)]);
  plots:-display( [seq( getODESol( 0.1, j, 3.5), j=0.3..1.0,0.1)]);
  plots:-display( [seq( getODESol( 0.1, 0.6, j), j=3..4,0.1)]);
#
# This one gernartes some singularity warnings which
# I haven't bothered to nail down - and I won't until
# the OP provides details of which combinations of
# parameters (s)he is interested in
#
  plots:-display( [ seq
                    ( seq
                      ( seq
                        ( getODESol( i, j, k),
                          i=0.5..0.7, 0.1
                        ),
                        j=0.5..0.7, 0.1
                      ),
                      k=3.4..3.6, 0.1
                    )
                   ]
                  );

 

 

 

Warning, cannot evaluate the solution further right of 19.820552, probably a singularity

 

Warning, cannot evaluate the solution further right of 19.926938, probably a singularity

 

Warning, cannot evaluate the solution further right of 19.494114, probably a singularity

 

Warning, cannot evaluate the solution further right of 19.785144, probably a singularity

 

 

 

 


 

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