Maple 2016 Questions and Posts

These are Posts and Questions associated with the product, Maple 2016

For my own use, I am attempting to port Joe Riel’s glyph package for geometric algebra into a module more compatible with recent versions of Maple. To this end, I have been testing individual procedures extracted from the package into Maple 2016, both to understand the algorithms and to check for glitches caused by the code running in more current Maple 2016. The procedure for carrying out the exterior multiplication of blades does not seem to work reliably, and I haven’t the necessary knowledge of Maple language to determine whether this is due to an error on my part or a feature of Maple V that no longer works.  I have attached a worksheet,tablemultiplyexample.mw,  that includes the procedures necessary for the multiplication routine to work, but I can’t get any consistency in the results.  Can anyone advise me what is the problem?  

As I understand the routine, setup defines a anti-symmetric root blade table with an indexing function that precludes assignment to the table. Clifford blades are then represented as indexed variables using the root table. The process is as follows see worksheet for actual code):

initialize := proc ()
 global _e, tableroot;
tableroot := table(antisymmetric, blade);
tableroot[] := 1;
_e := tableroot;
end proc:
#The index function `blade` is as follows:

`index/blade` := proc (Indices, tableau)
 if nargs = 2 then if Indices = [] then 1
          else tableau[op(checkindices(Indices))] end if
elif Indices = [] then tableau[Indices[]] := 1
 else ERROR("cannot assign to a blade", Indices) end if
end proc;

#Exterior multiplication is performed by the following routine.
b_exteriorp := proc (u, v)
option remember;
 if  u = 1 or v = 1 then u*v
else _e[op(u), op(v)] end if
end proc:

As near as I understand, the procedure joins the lists representing the two input blade into a single list that is processed by the antisymmetric indexing function and outputs the indexes as the product blade. I don’t understand how the case of duplicate indexes (which should return 0) is supposed to be handled by the procedure.  What the procedure usually returns is simply the appended list of the two blades without modification by the indexing function.

Can anyone give me a hint about how to fix this procedure?

tablemultiplyexample.mw

The question is sort of convoluted, but I hope somebody can help.

I have a data set I pulled from an Excel Sheet of the temperature for every day for a year.

Currently, it's in an Array 365x2, where the first column is what day of the year it is and the second column is the temperature. I want to create a plot that on the x-axis shows the day, but on the y-axis shows the amount of a certain chemical in the trees. I have a function of temperature vs chemicals, but I want my graph to show the day of the year vs amount of chemical. How would I go about making such a plot? I don't know how to connect all three. 

 

Thanks!

hello guys,
in the bellow, screen shot that I have sent to you.
how can I solve this three equations and obtain a1 a2 a3??? in fact non zero answers.
also is this possible to learn me how to write my codes that I have written in maple in the form that others send to you for their questions??? I dont know how to do that...and send screen shot!!
thank you

Hello,

I am confused by the Syntax of maple. When does maple numerically evaluates an expression? I know that maple cannot distinguish the variable "e" from the exponential function "e". So I have to use the command palette or enter the 1-D sequence "exp(1)". Maple shows the symbols if not told otherwise. I can numerically evaluate the expression using "evalf(exp(1))". 

But if I enter "I^2" for example maple behaves in a different way. It does not show "I^2" but it evaluates the expression. Same with "2+2". Maple shows me the result "4". So when does Maple numerically evaluate an expression and when does not?

Second question: When I enter "evalf(exp((I*2)*Pi))" I get "1.". What is the meaning of the point? Using "evalc(exp((I*2)*Pi))" I do not get the point - just "1".

Thank you in advance!

 

Hi

Please download and check the attached file.
It seems when you run the code more than one time, various results are obtained each time.

What is the reason? How it can be fixed?

Thanks


 

restart; Digits := 20; tm := time(); with(LinearAlgebra); m := 6; a := .1; b := 10*a; E := 1; h := 1; nu := .3; ur := -w*z+u0; u0 := 0; ut := add(add(T[n, i]*r^n*t^(i-n), n = 0 .. i), i = 0 .. m); w := (r-b)^2*(r-a)^2*add(add(W[n, i]*r^n*t^(i-n), n = 0 .. i), i = 0 .. m); er := diff(ur, r); et := ur/r+(diff(ut, t))/r; ert := 1/2*(diff(ut, r)-ut/r+(diff(ur, t))/r); u := -(1/2)*E*(2*er*et*nu+er^2+et^2)/(nu^2-1)+2*E*ert^2/(2+2*nu); N := sum(i+1, i = 0 .. m); PI := int(int(int(u*r, z = -(1/2)*h .. (1/2)*h), t = 0 .. 2*Pi), r = a .. b)-.5*P*(int(int(r*(diff(w, r))^2, r = a .. b), t = 0 .. 2*Pi)); s1 := seq(indets(add(add(T[n, i], n = 0 .. i), i = 0 .. m))[k] = c[k], k = 1 .. N); s2 := seq(indets(add(add(W[n, i], n = 0 .. i), i = 0 .. m))[k] = c[k+N], k = 1 .. N); PI := subs(s1, s2, PI); for k to 2*N do diff(PI, c[k]); if % = 0 then ex := `union`({}, {k}) else eq[k] := % end if end do; NE := seq(ex[j], j = 1 .. numelems(ex)); M := GenerateMatrix([`$`(eq[j], j = 1 .. 2*N)], [`$`(c[j], j = 1 .. 2*N)])[1]; M := DeleteColumn(DeleteRow(M, NE), NE); Determinant(M); 12*fsolve(%, P = 0 .. 1)*(-nu^2+1)*a^2/(E*h^3); Time = time()-tm

Time = 85.363

(1)

``


 

Download Stability.mw

hello guys, I can't take the real part of this formula that you can see in the picture that I upload for you.
please help me!!!!!!!!
sorry for uploading photo...so surry

Plot3d in this worksheet calls a procedure which conditionally returns the values for a parametrically defined ellipsoid, but the plot command fails. However the procedure passes the correct list of parametric values when it is called directly.

Is there a way to call a procedure within plot3d which successfully plots a parametrically defined surface?

Plot3d_proc_parametric.mw

Hello, everybody,

If I had the graph of a function just like plot(sin(x), x=-2..2)

The question is I want to plot this function is discrite form    by the pair of points (x[i], sin9x[i]) and i=1...N, where N is an integer number

The edges of the red and blue surfaces are ragged. Can they be made smoother when displayed?

Intersecting_surfaces.mw

Supposing as a nice simple example I use the power series command,

series(ex, x=0,8)

to get,

1+x+12x+ 16x+ 124x+ 1120x+ 1720x+ 15040x7

Is there automated anyway to get this as a Sigma representation? 

Hello, I have been attempting to plot a sequence of arrows in order to display how the vectors of the Frenet-Serret frame change throughout an helix-like trajectory. I came up with the following:

(With p1 being a plot I made earlier)

for t from 0 by 0.1e-1 to 12.5663706144 do plots[display](p1, plottools[arrow](Vector([cos(t), sin(t), t/(7.5)]), Vector([-(1/2)*sqrt(2)*sin(t), (1/2)*sqrt(2)*cos(t), (1/2)*sqrt(2)]), .1, .2, .3, cylindrical_arrow)) end do

This plots the desired arrow representing the tangent vector; however, it creates a plot for each step, while what I want is for it to display the arrow on each step in the same plot (as an animation).

I have attempted using the seq command, but I can't seem to get it right.

plots[display](p1, plottools[arrow](seq([Vector([cos(t), sin(t), t/(7.5)]), Vector([-(1/2)*sqrt(2)*sin(t), (1/2)*sqrt(2)*cos(t), (1/2)*sqrt(2)]), .1, .2, .3, cylindrical_arrow], t = 0 .. 4*Pi, 0.1e-1)))

With this code, the sequence won't be able to be executed.

Any ideas on how to do this? How can I use the sequence command in combination with plottools[arrow]?

Hello everyone.and complements

Please I am trying to obtain series expansion of the expression below in u but encounter difficulties particularly when b=0. I am very optimistic that when b=0 there will be a result not division by 0. Can I get help on the code?

Thank you in anticipation of your quick and positive responses and suggestions

# for k=2 CHEBY HYBRID WITH mu=(1-(1/2)*sqrt(2)))) AND v=(1+(1/2)*sqrt(2))))
restart:
omega:=u/h:
t:=(sum(a[j]*x^j,j=0..3)+a[4]*sin(omega*x)+a[5]*cos(omega*x)):
F:=diff(t,x):
G:=diff(t,x,x):
p1:=simplify(eval(t,x=q))=y[n]:
p2:=simplify(eval(t,x=q+(1-(1/2)*sqrt(2))*h))=y[n+mu]:
p3:=simplify(eval(t,x=q+h))=y[n+1]:
p4:=simplify(eval(t,x=q+(1+(1/2)*sqrt(2))*h))=y[n+v]:
p5:=simplify(eval(F,x=q+2*h))=f[n+2]:
p6:=simplify(eval(G,x=q+2*h))=g[n+2]:

vars:= seq(a[i],i=0..5):
Cc:=eval(<vars>, solve({p||(1..6)}, {vars})):
for i from 1 to 6 do
	a[i-1]:=Cc[i]:
end do:
Cf:=t:

K:=collect(combine(simplify(eval(Cf,x=q+2*h),size),trig),{y[n],y[n+mu],y[n+1],y[n+v],f[n+2], g[n+2]},factor):


Num := numer(K):
Den := denom(K):

N := 20:   # order of expansion
Num_N :=(convert(series(Num, u, N),polynom)):
Den_N := (convert(series(Den, u, N),polynom)):
b:=y[n+2]=(convert(series(Num_N/Den_N, u, N),polynom)):

eval(b,u=0); 

 

how can solve this nonlinear integral eq?

Hi there

I am trying to solve the ODE below

schechter_guo_v2.mw
 

odeSG := {diff(z(t), t) = (-phi*z(t)*sqrt(F*phi*z(t)/(5*t))/(3*t)+1-H/(1-z(t)))/(phi*(S_oi-S_or-sqrt(F*phi*z(t)/(5*t)))), z(t0) = z0}

{diff(z(t), t) = (-(1/15)*phi*z(t)*5^(1/2)*(F*phi*z(t)/t)^(1/2)/t+1-H/(1-z(t)))/(phi*(S_oi-S_or-(1/5)*5^(1/2)*(F*phi*z(t)/t)^(1/2))), z(t0) = z0}

(1)

solSG := dsolve(odeSG, numeric, method = lsode, parameters = [phi, F, H, S_oi, S_or, t0, z0])

proc (x_lsode) 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_lsode) else _xout := evalf(x_lsode) end if; _dat := Array(1..4, {(1) = proc (_xin) local _xout, _n, _y0, _ctl, _octl, _reinit, _errcd, _fcn, _i, _yini, _pars, _ini, _par; option `Copyright (c) 2002 by the University of Waterloo. All rights reserved.`; table( [( "complex" ) = false ] ) _xout := _xin; _ctl := array( 1 .. 39, [( 1 ) = (1), ( 2 ) = (t0), ( 3 ) = (t0), ( 4 ) = (1), ( 5 ) = (1), ( 6 ) = (10), ( 7 ) = (0), ( 9 ) = (0.1e-6), ( 8 ) = (z0), ( 11 ) = (0), ( 10 ) = (0.1e-6), ( 13 ) = (0), ( 12 ) = (0), ( 15 ) = (0), ( 14 ) = (0), ( 18 ) = (0), ( 19 ) = (0), ( 16 ) = (0), ( 17 ) = (0), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = (0), ( 21 ) = (0), ( 27 ) = (0), ( 26 ) = (0), ( 25 ) = (0), ( 24 ) = (0), ( 31 ) = (-1), ( 30 ) = (0), ( 29 ) = (0), ( 28 ) = (0), ( 36 ) = (0), ( 37 ) = (0), ( 38 ) = (0), ( 39 ) = (0), ( 32 ) = (7), ( 33 ) = (0), ( 34 ) = (0), ( 35 ) = (0)  ] ); _octl := array( 1 .. 39, [( 1 ) = (1), ( 2 ) = (t0), ( 3 ) = (t0), ( 4 ) = (1), ( 5 ) = (1), ( 6 ) = (10), ( 7 ) = (0), ( 9 ) = (0.1e-6), ( 8 ) = (z0), ( 11 ) = (0), ( 10 ) = (0.1e-6), ( 13 ) = (0), ( 12 ) = (0), ( 15 ) = (0), ( 14 ) = (0), ( 18 ) = (0), ( 19 ) = (0), ( 16 ) = (0), ( 17 ) = (0), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = (0), ( 21 ) = (0), ( 27 ) = (0), ( 26 ) = (0), ( 25 ) = (0), ( 24 ) = (0), ( 31 ) = (-1), ( 30 ) = (0), ( 29 ) = (0), ( 28 ) = (0), ( 36 ) = (0), ( 37 ) = (0), ( 38 ) = (0), ( 39 ) = (0), ( 32 ) = (7), ( 33 ) = (0), ( 34 ) = (0), ( 35 ) = (0)  ] ); _n := trunc(_ctl[1]); _yini := Array(0..8, {(1) = t0, (2) = z0, (3) = undefined, (4) = undefined, (5) = undefined, (6) = undefined, (7) = undefined, (8) = undefined}); _y0 := Array(0..8, {(1) = t0, (2) = z0, (3) = undefined, (4) = undefined, (5) = undefined, (6) = undefined, (7) = undefined, (8) = undefined}); _fcn := proc (N, X, Y, YP) option `[Y[1] = z(t)]`; if Y[3]*Y[2]*Y[1]/X < 0 then YP[1] := undefined; return 0 end if; YP[1] := (-.149071198499986*Y[2]*Y[1]*evalf((Y[3]*Y[2]*Y[1]/X)^(1/2))/X+1-Y[4]/(1-Y[1]))/(Y[2]*(Y[5]-Y[6]-.447213595499958*evalf((Y[3]*Y[2]*Y[1]/X)^(1/2)))); 0 end proc; _pars := [phi = phi, F = F, H = H, S_oi = S_oi, S_or = S_or, t0 = t0, z0 = z0]; if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then return _y0[0] elif _xout = "method" then return "lsode" elif _xout = "numfun" then return trunc(_ctl[24+trunc(_ctl[1])]) elif _xout = "initial" then return [seq(_yini[_i], _i = 0 .. _n)] elif _xout = "parameters" then return [seq(_yini[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return [seq(_yini[_i], _i = 0 .. _n)], [seq(_yini[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _ctl[2]-_y0[0] = 0. then error "no information is available on last computed point" else _xout := _ctl[2] end if elif _xout = "enginedata" then return eval(_octl, 1) elif _xout = "function" then return eval(_fcn, 1) 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); if _par <> [] then `dsolve/numeric/process_parameters`(_n, _pars, _par, _yini) end if; if _ini <> [] then `dsolve/numeric/process_initial`(_n, _ini, _yini, _pars) end if; if _pars <> [] then _par := {seq(rhs(_pars[_i]) = _yini[_n+_i], _i = 1 .. nops(_pars))}; for _i from 0 to _n do _y0[_i] := subs(_par, _yini[_i]) end do; for _i from _n+1 to _n+nops(_pars) do _y0[_i] := _yini[_i] end do else for _i from 0 to _n do _y0[_i] := _yini[_i] end do end if; _octl[2] := _y0[0]; _octl[3] := _y0[0]; for _i to _n do _octl[_i+7] := _y0[_i] end do; for _i to nops(_pars) do _octl[2*_n+30+_i] := _y0[_n+_i] end do; for _i to 39 do _ctl[_i] := _octl[_i] end do; if _Env_smart_dsolve_numeric = true and type(_y0[0], 'numeric') then procname("right") := _y0[0]; procname("left") := _y0[0] end if; if _xout = "initial" then return [seq(_yini[_i], _i = 0 .. _n)] elif _xout = "parameters" then return [seq(_yini[_n+_i], _i = 1 .. nops(_pars))] else return [seq(_yini[_i], _i = 0 .. _n)], [seq(_yini[_n+_i], _i = 1 .. nops(_pars))] end if else return "procname" end if end if; if _xout-_y0[0] = 0. then return [seq(_y0[_i], _i = 0 .. _n)] end if; _reinit := false; if _xin <> "last" then if 0 < 0 and `dsolve/numeric/checkglobals`(0, table( [ ] ), _pars, _n, _yini) then _reinit := true; if _pars <> [] then _par := {seq(rhs(_pars[_i]) = _yini[_n+_i], _i = 1 .. nops(_pars))}; for _i from 0 to _n do _y0[_i] := subs(_par, _yini[_i]) end do; for _i from _n+1 to _n+nops(_pars) do _y0[_i] := _yini[_i] end do else for _i from 0 to _n do _y0[_i] := _yini[_i] end do end if; for _i to _n do _octl[_i+7] := _y0[_i] end do; for _i to nops(_pars) do _octl[2*_n+30+_i] := _y0[_n+_i] end do end if; if _pars <> [] and select(type, {seq(_yini[_n+_i], _i = 1 .. nops(_pars))}, 'undefined') <> {} then error "parameters must be initialized before solution can be computed" end if end if; if not _reinit and _xout-_ctl[2] = 0 then [_ctl[2], seq(_ctl[_i], _i = 8 .. 7+_n)] else if sign(_xout-_ctl[2]) <> sign(_ctl[2]-_y0[0]) or abs(_xout-_y0[0]) < abs(_xout-_ctl[2]) or _reinit then for _i to 39 do _ctl[_i] := _octl[_i] end do end if; _ctl[3] := _xout; if Digits <= evalhf(Digits) then try _errcd := evalhf(`dsolve/numeric/lsode`(_fcn, var(_ctl))) catch: userinfo(2, `dsolve/debug`, print(`Exception in lsode:`, [lastexception])); if searchtext('evalhf', lastexception[2]) <> 0 or searchtext('real', lastexception[2]) <> 0 or searchtext('hardware', lastexception[2]) <> 0 then _errcd := `dsolve/numeric/lsode`(_fcn, _ctl) else error  end if end try else _errcd := `dsolve/numeric/lsode`(_fcn, _ctl) end if; if _errcd < 0 then userinfo(2, {dsolve, `dsolve/lsode`}, `Last values returned:`); userinfo(2, {dsolve, `dsolve/lsode`}, ` t =`, _ctl[2]); _i := 8; userinfo(2, {dsolve, `dsolve/lsode`}, ` y =`, _ctl[_i]); for _i from _i+1 to 7+_n do userinfo(2, {dsolve, `dsolve/lsode`}, `	 `, _ctl[_i]) end do; if _errcd+1. = 0. then if _ctl[14+trunc(_ctl[1])] <> 0 then error "an excessive amount of work was done, maxstep may be too small" else error "an excessive amount of work (greater than mxstep) was done" end if elif _errcd+2. = 0. then error "too much accuracy was requested for the machine being used" elif _errcd+3. = 0. then error "illegal input was detected" elif _errcd+4. = 0. then error "repeated error test failures on the attempted step" elif _errcd+5. = 0. then error "repeated convergence test failures on the attempted step" elif _errcd+6. = 0. then error "pure relative error control requested for a variable that has vanished" elif _errcd+7. = 0. then error "cannot evaluate the solution past %1, maxfun limit exceeded (see <a href='http://www.maplesoft.com/support/help/search.aspx?term=dsolve,maxfun' target='_new'>?dsolve,maxfun</a> for details)", evalf[8](_ctl[2]) else error "unknown error code returned from lsode %1", trunc(_errcd) end if end if; if _Env_smart_dsolve_numeric = true then if _y0[0] < _xout and procname("right") < _xout then procname("right") := _xout elif _xout < _y0[0] and _xout < procname("left") then procname("left") := _xout end if end if; [_xout, seq(_ctl[_i], _i = 8 .. 7+_n)] end if end proc, (2) = Array(0..0, {}), (3) = [t, z(t)], (4) = [phi = phi, F = F, H = H, S_oi = S_oi, S_or = S_or, t0 = t0, z0 = z0]}); _vars := _dat[3]; _pars := map(rhs, _dat[4]); _n := nops(_vars)-1; _solnproc := _dat[1]; if not type(_xout, 'numeric') then if member(x_lsode, ["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_lsode, '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_lsode, ["last", 'last', "initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(x_lsode, '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_lsode), 'string') = rhs(x_lsode); 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_lsode), 'string') = rhs(x_lsode)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _vars end if; if procname <> unknown then return ('procname')(x_lsode) else _ndsol; _ndsol := pointto(_dat[2][0]); return ('_ndsol')(x_lsode) end if end if; try _res := _solnproc(_xout); [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] catch: error  end try end proc

(2)

solSG(parameters = [.1, 1, .1, 1, .1, 0.1e-3, 0])

[phi = .1, F = 1., H = .1, S_oi = 1., S_or = .1, t0 = 0.1e-3, z0 = 0.]

(3)

``

Loading plots

odeplot(solSG, t = 0.1e-3 .. 10)

 

plots:-odeplot(solSG, t = 0.1e-3 .. 1)

 

plots:-odeplot(solSG, t = 0.1e-3 .. .1)

 

``


 

Download schechter_guo_v2.mw

My questions are:

1. Why does the solution for the longer time span (t<10) looks different from the shorter time span (t<0.1)? I have read about stiff ODEs and probably this has something to do with it. I am trying to figure out what is going on with the solutions.

2. I tried dsolve with stiff methods (lsode and rosenbrock) and both gave me the same solutions as above. I have not tried the advance options yet. How do I set dsolve so that the solution for the longer span (t>10) looks similar to shorter span?

Many thanks for your answers/suggestions.

 

I would like procedure P to perform inside the map statement exactly as it does outside the map statement. Can this be done?

Map_Procedure.mw

 

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