Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Hi, 

Could anyone help me to numerically solve this ode?
I've tried almost all the methods Maple proposes, trying to adjust stepsizes, tolerances and so on;, always without success.

I give also the exact solution of this ode in order to compare the numerical solution to.

Thanks in advance
 

restart

interface(version)

`Standard Worksheet Interface, Maple 2015.2, Mac OS X, December 21 2015 Build ID 1097895`

(1)

with(plots):

# Source term

F := t*(-600*t/(100*t^2+1)^2+80000*t^3/(100*t^2+1)^3)/(100*t^2+1)-(1/(100*t^2+1)-200*t^2/(100*t^2+1)^2)/(1+(1/(100*t^2+1)-200*t^2/(100*t^2+1)^2)^2);

plot(F, t=0..0.5);

t*(-600*t/(100*t^2+1)^2+80000*t^3/(100*t^2+1)^3)/(100*t^2+1)-(1/(100*t^2+1)-200*t^2/(100*t^2+1)^2)/(1+(1/(100*t^2+1)-200*t^2/(100*t^2+1)^2)^2)

 

 

# Ode

ode := X(t)*diff(X(t), t$2)-diff(X(t),t)/(1+diff(X(t),t)^2) - 'F'

X(t)*(diff(diff(X(t), t), t))-(diff(X(t), t))/(1+(diff(X(t), t))^2)-F

(2)

# Initial conditions

ics := X(0) = 0, D(X)(0) = 1

X(0) = 0, (D(X))(0) = 1

(3)

# I used alot methods with allways either failure or either a HFloat(undefined)

printf("rkf45\n");
sol := dsolve({ode, ics}, numeric):
sol(1e-8);

printf("\n\nrosenbrock\n");
sol := dsolve({ode, ics}, numeric, method=rosenbrock):
sol(1e-8);

printf("\n\ngear\n");
sol := dsolve({ode, ics}, numeric, method=gear):
sol(1e-8);

printf("\n\ngear\n");
sol := dsolve({ode, ics}, numeric, method=classical[heunform]):
sol(1e-8);

rkf45

Error, (in sol) cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

 



rosenbrock

Error, (in dsolve/numeric/SC/firststep) unable to evaluate the partial derivatives of f(x,y) for stiff solution

 

Error, (in sol) cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

 



gear

 

[t = 0.1e-7, X(t) = HFloat(HFloat(undefined)), diff(X(t), t) = HFloat(HFloat(undefined))]

 



gear

 

[t = 0.1e-7, X(t) = HFloat(HFloat(undefined)), diff(X(t), t) = HFloat(HFloat(undefined))]

(4)

# The solution must be this one

U := t -> t/((t*10)^2+1)

proc (t) options operator, arrow; t/(100*t^2+1) end proc

(5)

# Check ode and ics

eval(ode, X(t)=U(t));
U(0);
D(U)(0);

0

 

0

 

1

(6)

# Plots when a solution is obtained

display(
  plot(U(t), t=0..1, color=blue),
  odeplot(sol, [t, x(t)], t=0..1, color=red, linestyle=3)
);


 

Download Unsuccessful_dsolve.mw

 

xE.mw

I integrate the expression maple but the result is large. How to furtherxE.mw reduce the size of the result? Also, what is dilog on maple?

I am creating Maple figures that are being used to create camera-ready figures in Adobe Illustrator. The graphic artist doing the Adobe Illustrator has asked me if there is a way to have the text information in the figure (tickmarks, axis labels, ...) saved as text and not created as an image?

I know that other EPS files have text stored this way, but it appears Maple does not do this. I can't find any documentation about this. Does anybody have any knowledge or experience about this?

Thanks in advance,

Doug

Or has the Maple destroyed my Maple Document beyond repair? I remember that part from Mathematica, the part where they force you to save your document in their propriety format and then one day their editor becomes unable to edit its own propriety format, so there's no workaround, and you lose a month of work and feel like throwing up and you're paralyzed by hatred for the people who sold you this.

In my worksheet today my intention was to compare the least squares linear regression for three datasets as indicated, but when I right click on the output as seen in the bottom line to select the plot type, all options state there to be independant variables K[0] and K[1], where as the output displays only the variable K as I intended, which part of my code is creating this confusion for maple?

 

 

 

Worksheet Specific Investigation Content

 

S[0] := proc (N, K) options operator, arrow; map(simplify, {seq(seq(seq(piecewise((a^`ϕ`(b))^(1/(c+1))-floor((a^`ϕ`(b))^(1/(c+1))) = 0, [a, b, c], NULL), a = 1 .. N), b = 1 .. N), c = 1 .. K)}, 'radical') end proc

T := proc (N, K) options operator, arrow; {seq(seq(seq([a, b, c], a = 1 .. N), b = 1 .. N), c = 1 .. K)} end proc:

S[1] := proc (N, K) options operator, arrow; `minus`(T(N, K), S[0](N, K)) end proc:

CardRatio := proc (N, K) options operator, arrow; nops(S[0](N, K))/nops(S[1](N, K)) end proc:

{CurveFitting[LeastSquares]([seq([k, CardRatio(2, k)], k = 1 .. 10)], K), CurveFitting[LeastSquares]([seq([k, CardRatio(3, k)], k = 1 .. 10)], K), CurveFitting[LeastSquares]([seq([k, CardRatio(4, k)], k = 1 .. 10)], K)}

{1, 44268857/45401356-(532409481/9988298320)*K, 24308311919/13309971675-(135902619982/773879781675)*K}

(1.1)

``

 

 

 

 

Download ask_maple.mw

 

 

I want to do the substitution f(t) - ff(t) = epsilon for any variable t in Maple:

 

expand(myerror);
    2 f(x - 2 h)   f(x)   3 f(x + 3 h)   2 ff(x - 2 h)   ff(x)
  - ------------ - ---- + ------------ + ------------- + -----
        15 h       6 h        10 h           15 h         6 h

       3 ff(x + 3 h)
     - -------------
           10 h     


NULL;
myfunc := t -> f(t) - ff(t) = epsilon;
 myfunc := proc (t) options operator, arrow, function_assign;

    f(t)-ff(t) = epsilon end proc


algsubs(myfunc(t), myerror);
          2               1        3            
        - -- f(x - 2 h) - - f(x) + -- f(x + 3 h)
          15              6        10           
        ----------------------------------------
                           h                    

               2                1         3             
             - -- ff(x - 2 h) - - ff(x) + -- ff(x + 3 h)
               15               6         10            
           - -------------------------------------------
                                  h                     


NULL;
subs(f(-h*n + x) = 1, ff(-h*n + x) = 0, f(x) = 1, ff(x) = 0, f(h*m + x) = 1, ff(h*m + x) = 0, myerror)*epsilon;
                           4 epsilon
                           ---------
                             15 h   

 

This happens each time I run a long loop.  (2,500 iterations, which takes about 3 hrs to complete)

Maple always hangs (it does not time out on odetest() ). But my question is not about this (as this is something I have to deal with for long time now and mentioned it before many times. May be one day Maplesoft will fix this). 

But I noticed this also.  When Maple hangs, (and it always hangs at least once during this loop), I then click on the button "interrupt the current operation". This does stop the hangs.

Next I do a restart and starts the loop from the loop counter where it hanged in order to continue.  

But It still hangs at that same iteration. I repeate this again, and it still hangs.

Now I close Maple altogether, start Maple again, open same worksheet, and repeat from the same iteration again from where it was at before, now it does not hang.

This tells me that restart and "interrupt the current operation" do not clean everything as expected. Else why only restarting Maple makes it work?

It means mserver.exe (separate process from the frontend) still is caching something related, and that is why it hangs at that iteration.

I can reproduce this each time I run the whole loop from the start.

I can't make a minimal example, since I have no idea where it hangs and why. And it is related to running a long loop.

I just know it hangs when doing odetest() with timeout which never timeout, and it seems random at what iteration it decides to hang.

But my question is really basic here: Does mserver.exe keep any information about the earlier user session/worksheet even after restart ? help says that restarts clear internal memory of the kernel.

Isn't mserver.exe  the Maple kernel? If so, then what could explain that only restarting Maple clears the hang? I am just looking for ideas that could explain this.

This type of problem is the most annoying thing about Maple for me. 

Maple 2020.1 on windows 10.

 


Eigenvector result is changing every time it run.

How to make eigenvectors result the same every time it run?

 

What do I need to do to the "2 + 3" in the attached Document in order to make it evaluate? I know about F5 to switch between Text and Math modes, but that's not enough to get me where I want to be. The "2 + 3" is already in Math mode, but that's not enough to get it to evaluate.

The Document: t.mw

Something goes wrong in this worksheet with old code

Must be corrected
Thanks

fmatrix.mws

Anyone maybe helps me with writing the maple code mentioned in the following pdf.

I want to know about the potential flow around 3D domain.

 

Doc1.pdf

Don't get a DEplot 


 

with(DEtools,DEplot);with(plots,display);

[DEplot]

 

[display]

(1)

 

 

 

init3:=seq([0,k*0.2,0],k=-4..10);

[0, -.8, 0], [0, -.6, 0], [0, -.4, 0], [0, -.2, 0], [0, 0., 0], [0, .2, 0], [0, .4, 0], [0, .6, 0], [0, .8, 0], [0, 1.0, 0], [0, 1.2, 0], [0, 1.4, 0], [0, 1.6, 0], [0, 1.8, 0], [0, 2.0, 0]

(2)

 

The forward plot is p3:

 

p3:=DEplot([sys],[x,y],t=0..2,[init3],x=-3..2,y=-3..2,stepsize=.05,arrows=none,linecolor=black,thickness=1,axes=box,scaling=constrained):

Error, (in f) numeric exception: division by zero

 

he backward plot is np3:

 

np3:=DEplot([sys],[x,y],t=-2..0,[init3],x=-3..2,y=-3..2,stepsize=.05,arrows=none,linecolor=black,thickness=1,axes=box,scaling=constrained):

Warning, plot may be incomplete, the following errors(s) were issued:
   cannot evaluate the solution further left of -.29861232, probably a singularity
Warning, plot may be incomplete, the following errors(s) were issued:
   cannot evaluate the solution further left of -.93147185e-1, probably a singularity
Warning, plot may be incomplete, the following errors(s) were issued:
   cannot evaluate the solution further left of -.23648931e-1, probably a singularity
Warning, plot may be incomplete, the following errors(s) were issued:
   cannot evaluate the solution further left of -.27325542e-2, probably a singularity

 

Error, (in f) numeric exception: division by zero

 

 

display({p1,p2,p3,np3});

Error, (in plots:-display) expecting plot structures but received: {np3}

 

 


 

Download uitzoeken_ode_lesmateriaal_betounes_of_het_werkt.mw

Hi,

How I can solve biharmonic equations in toroidal coordinate?

If this possible I can provide a worksheet and send it.

I provided a solution for Laplacian in pdf file.

Separation_of_Laplace.pdf

Dear maple users,

Greetings.

When converting the maple figure into EPS format (for latex) which shows white patches.

How to avoid such patches.

Hello everyone.

I am not really sure how to solve the following problem:

Given a parametriaztion of a surface as an interpolation in terms of given nodes as:
X(ξ,η)= Σ Νi(ξ,η) Xi, it is possible to calculate tangent and normal vectors as:
α1(ξ,η)= Σ Νi,ξ(ξ,η) Xi     α2(ξ,η)= Σ Νi,η(ξ,η) Xi  and a3(ξ,η)= cross(a1,a2) and their derivatives
α1,ξ α1,η α2,ξ α2,η etc.
For a variation of Xi i.e.  a variation of X can be calculated δX(ξ,η)= Σ Νi(ξ,η) δXi in terms of 
intermediate quantities that are as simple as  Σ Νi(ξ,η) for the position vector but get quite complicate
for the normal vector (δα3 that depends on a cross product) of given vectors  and for higher order derivatives,
or for the second variation. These variations can be also expressed with a directional derivative in the direction 
X,Y, or Z of a node i with initial position Xi.

To calculate those more complicate derivations I try to express them in terms of known less complicate ones.
Symbolizing r and s the first and second variation, and α,β firs and second derivative withh respect to ξ οr h or ξ,η.


Regarding the variation of the normal vector "a3_t" as known (i.e. a3_t,r)
and the variation of its norm "a3_n" (i.e. a3_n,r) as known too we can get the variation of
the of unit normal using the following commands:

a3 := a3_t(a, s, r)*(1/a3_n(a, s, r)): (vector-scalar operation) (1)
diff(a3, r):

the second variation
diff(a3, r):
diff(diff(a3, r), s) (2)

and even variations of its derivatives 
diff(diff(diff(a3, a), r), s): (3) 

That yield the results of the posted picture.

The problem is that if we want to calculate in the same way the variation of the derivative 
of expressions that involve the vector-vector operations i.e  variation of diff(a3_t, a)
where a3_t = CrossProduct(a1(a,r,s),a2(a,r,s)) it is not possible to do that as in (1)
we cannot substitute CrossProduct or dot product operation  with simple multiplication.

If we use the same strategy in VectorCalculus package we can get some results:
using the following commands: 

a1 := PositionVector([a1x(a, s, r), a1y(a, s, r), a1z(a, s, r)], cartesian[x, y, z])
a2 := PositionVector([a2x(a, s, r), a2y(a, s, r), a2z(a, s, r)], cartesian[x, y, z])
a3T := CrossProduct(a1, a2)
diff(a3T, r)

but then (as it is shown in the upload picture 2) the calculations are performed component-wise
are very lengthy so it is impossible to get second derivative or second derivation.

So I would like to ask is it possible to declare a1 as a vector but not give its components a1x, a1y etc explicitely but instead
declare it as a vector valued function of (a, r, s). so that it yields simpler expressions 
as "a3_t,r= a1,r(x)a2 + a1(x)a2,r".

I would also like to know if those calculations can be made simpler with and another package and if so is there an appropriate example
or a book that explains how to do that.

I would really appreciate  any idea.
Because this is a difficult problem Maple can make it very easy.

Thank you in advance.


upload1.mw

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