Maple 2024 Questions and Posts

why am I getting "insufficient initial/boundary va...

Asked by: Tom GIV 25

February 04 2025

1 4

I'm trying to solve a system of two differential equations numerically

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Error, (in dsolve/numeric/type_check) insufficient initial/boundary value information for procedure defined problem

It seems to me this problem should be solvable for the initial conditions given. Am I entering them wrong somehow?

Download dsolve_problem.mw

How to get solution Soll11 for the reduced Liouvil...

Asked by: janhardo 675

February 02 2025

0 5

The modified Liouville equation

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How to solve this pde for a general solution ?

The general solution in this form exist.

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restart;

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with(PDEtools): declare(u(x,t)); U:=diff_table(u(x,t));
PDE1:=U[t,t]=a^2*U[x,x]+b*exp(beta*U[]);
Sol11:=u(x,t)=1/beta*ln(2*(B^2-a^2*A^2)/(b*beta*(A*x+B*t+C)^2));
Sol12:=S->u(x,t)=1/beta*ln(8*a^2*C/(b*beta))
-2/beta*ln(S*(x+A)^2-S*a^2*(t+B)^2+S*C);
Test11:=pdetest(Sol11,PDE1);
Test12:=pdetest(Sol12(1),PDE1);
Test13:=pdetest(Sol12(-1),PDE1);

u(x, t) = ln(2*(-A^2*a^2+B^2)/(b*beta*(A*x+B*t+C)^2))/beta

proc (S) options operator, arrow; u(x, t) = ln(8*a^2*C/(b*beta))/beta-2*ln(S*(x+A)^2-S*a^2*(t+B)^2+S*C)/beta end proc

(1)

The Soll11 can be plotted with a Explore plot in this form of soll11 with th eparameters , but suppose i try to get the general solution in Maple ?

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>	ans := pdsolve(PDE1);

What solvin gstrategy to follow ? : the pde is a non-linear wave eqation with a exponentiel sourceterm
It seems that the pde can reduced to a ode? :

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with(PDEtools):
declare(u(x,t));

# Stap 1: Definieer de PDE
PDE := diff(u(x,t), t,t) = a^2 * diff(u(x,t), x,x) + b * exp(beta * u(x,t));

# Stap 2: Definieer de transformatie naar karakteristieke variabelen
# Nieuw: x en t uitgedrukt in ξ en η
tr := {
    x = (xi + eta)/2,
    t = (eta - xi)/(2*a)
};

# Pas de transformatie toe op de PDE
simplified_PDE := dchange(tr, PDE, [xi, eta], params = [a, b, beta], simplify);

# Stap 3: Definieer de algemene oplossing
solution := u(x,t) = (1/beta) * ln(
    (-8*a^2/(b*beta)) *
    diff(_F1(x - a*t), x) * diff(_F2(x + a*t), x) /
    (_F1(x - a*t) + _F2(x + a*t))^2
);

# Stap 4: Controleer de oplossing (optioneel)
pdetest(solution, PDE); # Moet 0 teruggeven als correct

u(x, t) = ln(-8*a^2*(D(_F1))(-a*t+x)*(D(_F2))(a*t+x)/(b*beta*(_F1(-a*t+x)+_F2(a*t+x))^2))/beta

(2)

missing some steps here : solution u without the pde reduced ?
there is a ode ?

>	# Definieer de ODE # vorige stappen ontbreken van de reduktie ode := (v^2 - a^2) * diff(f(xi), xi, xi) = b * exp(beta * f(xi)); # Algemene oplossing zoeken sol := dsolve(ode, f(xi));

f(xi) = ln((1/2)*c__1*(tan((1/2)*(-c__1*a^2*beta+c__1*beta*v^2)^(1/2)*(c__2+xi)/(a^2-v^2))^2+1)/b)/beta

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, ,

Question : how do i arrive on Soll11 in Maple ?

Download liouville_reduced_2-2-2025_mprimes_vraag.mw

Where to set stack size and heap limit...

Asked by: segfault 145

February 01 2025

1 11

I read the install.html that is installed with Maple2024 and the instructions to increase stack and heap limits are definately outdated.

None of the files they list there for Linux even exists after the Maple2024 installation.

So where exactly can I set the stack and heap size limits on Linux, as Maple give me stack and heap errors.

How find phase shift parameter in solution of PDE ...

Asked by: salim-barzani 1550

January 30 2025

0 16

It been a while i try to figure out How they find dispersion parameter and phase shift i figure out how find dispersion in some of pde but some of them is not give me even dispresion parameter i don't know they wrong or i am , but for finding phase shift there is three cenarios, when we change pde to bilinear form we have linear term in bilinear form so after substitute in linear term f bilinear form we can get dispersion parameter which is a parameter beside (t) also we can generalized for all of solution by changing the number of parameter as mention in the paper, but for phase shift parameter i don't know how find it i must substitute our solution in linear term or whole bilinear form of in first pde linear term i try all but i don't know what is i did mistake the paper say put in pde but i think he mention the the bilinear form i did all part for one soliton is w[1] for 2soliton is w[2] file i just want find parameter a[12] in paper for 2-soliton eq(19) then i will find for other just i need to find one of them, thanks for any help in this topic .

How to show symbolically that eigenvalues are the ...

Asked by: dharr 8045

January 29 2025

3 6

I am trying to show that the eigenvalues of a matrix are described by my proposed formula. I managed to show this numerically, but I would like to show this symbolically. There are two issues here - the orders of the two lists are different, and the forms are different (sums of complex exponentials vs RootOfs). Any suggestions?

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restart;

>	with(LinearAlgebra): with(GraphTheory): with(plots):

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L:=9;

Generate a matrix and its eigenvalues

>	C := AdjacencyMatrix(CycleGraph(L, directed)): Id := IdentityMatrix(L): A := KroneckerProduct(C, Id) + KroneckerProduct(Id, C) + KroneckerProduct(C, C): evs := Eigenvalues(A, output = list): plotevs := complexplot(evs, style = point, color = blue, scaling = constrained):

My guess as to their values

>	evstheory:=[seq(seq(exp((2Pi)Ik/L) + exp((2Pi)Im/L) + exp((2Pi)I*(m + k)/L), k = 0 .. L - 1), m = 0 .. L - 1)]: plotevstheory:=complexplot(evstheory, style = point, color = red, scaling = constrained):

They look to be the same

>	display(Array([plotevs,plotevstheory]));

Even showing they are the same numerically is nontrivial because the sorting is not consistent

>	fnormal(sort(evalf(evs))-sort(evalf(evstheory)));

This succeeds, so they are the same

>	fnormal(sort(evalf[20](evs),key=evalf)-sort(evalf[20](evstheory),key=evalf));

What about symbolically? [Edit - only part of output shown]

>	ans1:=simplify(sort(evs,key=evalf)-sort(evstheory,key=evalf));

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Download verification.mw

How find true parameter which satisfy pde?...

Asked by: salim-barzani 1550

January 28 2025

0 2

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LL := diff(diff(diff(diff(diff(f(x, y, z, t), x), x), x), x), x)-(diff(diff(diff(f(x, y, z, t), x), x), x))-(diff(diff(diff(f(x, y, z, t), t), t), x))-(diff(diff(diff(f(x, y, z, t), t), x), x))-2*(diff(diff(diff(f(x, y, z, t), t), x), y))-(diff(diff(diff(f(x, y, z, t), x), x), y))-(diff(diff(diff(f(x, y, z, t), x), x), z))-(diff(diff(diff(f(x, y, z, t), x), y), y)) = 0

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S22 := f(x, y, z, t) = 1+exp((-(1/2)*k[1]-l[1]+(1/2)*sqrt(4*k[1]^4-3*k[1]^2-4*k[1]*s[1]))*t+k[1]*x+l[1]*y+s[1]*z)+exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*sqrt(4*k[2]^4-3*k[2]^2-4*k[2]*s[2]))*t)+B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*sqrt(4*k[1]^4-3*k[1]^2-4*k[1]*s[1]))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*sqrt(4*k[2]^4-3*k[2]^2-4*k[2]*s[2]))*t)

f(x, y, z, t) = 1+exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z)+exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)+B[1]*exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)

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${t, x, y, z, B[1], k[1], k[2], l[1], l[2], s[1], s[2], (4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2), (4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2), exp(k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t), exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z), exp((-(1/2)*k[1]-l[1]+(1/2)*(4*k[1]^4-3*k[1]^2-4*k[1]*s[1])^(1/2))*t+k[1]*x+l[1]*y+s[1]*z+k[2]*x+l[2]*y+s[2]*z+(-(1/2)*k[2]-l[2]+(1/2)*(4*k[2]^4-3*k[2]^2-4*k[2]*s[2])^(1/2))*t)}$

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>

eq2 := algsubs(exp((-(1/2)*k[1]-l[1]+(1/2)*sqrt(4*k[1]^4-3*k[1]^2-4*k[1]*s[1]))*t+k[1]*x+l[1]*y+s[1]*z) = X, L4)

(11)

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-(1/2)*(k[1]+k[2])*B[1]*((k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)-8*k[1]*k[2]^3-12*k[2]^2*k[1]^2+(-8*k[1]^3+3*k[1]+2*s[1])*k[2]+2*s[2]*k[1])*exp((1/2)*t*(k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*(-k[1]-k[2]-2*l[1]-2*l[2])*t+k[1]*x+k[2]*x+l[1]*y+l[2]*y+z*(s[1]+s[2])) = 0

(12)

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${t, x, y, z, B[1], k[1], k[2], l[1], l[2], s[1], s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2), exp((1/2)*t*(k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2)+(1/2)*t*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+(1/2)*(-k[1]-k[2]-2*l[1]-2*l[2])*t+k[1]*x+k[2]*x+l[1]*y+l[2]*y+z*(s[1]+s[2]))}$

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eq4 := algsubs(exp((1/2)*t*sqrt(k[1]*(4*k[1]^3-3*k[1]-4*s[1]))+(1/2)*t*sqrt(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))+(1/2)*(-k[1]-k[2]-2*l[1]-2*l[2])*t+k[1]*x+k[2]*x+l[1]*y+l[2]*y+z*(s[1]+s[2])) = V, eq3)

-(1/2)*(k[1]+k[2])*B[1]*(-8*k[2]*k[1]^3-12*k[2]^2*k[1]^2-8*k[1]*k[2]^3+(k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+3*k[1]*k[2]+2*s[2]*k[1]+2*s[1]*k[2])*V = 0

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${V, B[1], k[1], k[2], s[1], s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}$

(15)

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eqs := {coeffs(collect(numer(normal(lhs(eq4))), {V}, 'distributed'), {V})}; nops(%); indets(eqs)

${-(k[1]+k[2])*B[1]*(-8*k[2]*k[1]^3-12*k[2]^2*k[1]^2-8*k[1]*k[2]^3+(k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)+3*k[1]*k[2]+2*s[2]*k[1]+2*s[1]*k[2])}$

${B[1], k[1], k[2], s[1], s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}$

(16)

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${B[1], k[1], k[2], s[1], s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}$

Warning, solving for expressions other than names or functions is not recommended.

${B[1] = B[1], k[1] = -k[2], k[2] = k[2], s[1] = s[1], s[2] = s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2) = (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2) = (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}, {B[1] = 0, k[1] = k[1], k[2] = k[2], s[1] = s[1], s[2] = s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2) = (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2) = (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}, {B[1] = B[1], k[1] = k[1], k[2] = k[2], s[1] = (1/2)*(8*k[2]*k[1]^3+12*k[2]^2*k[1]^2+8*k[1]*k[2]^3-3*k[1]*k[2]-2*s[2]*k[1]-(k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2)*(k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2))/k[2], s[2] = s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2) = (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2) = (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}$

(17)

>

${B[1] = B[1], k[1] = -k[2], k[2] = k[2], s[1] = s[1], s[2] = s[2], (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2) = (k[1]*(4*k[1]^3-3*k[1]-4*s[1]))^(1/2), (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2) = (k[2]*(4*k[2]^3-3*k[2]-4*s[2]))^(1/2)}$

(18)

>

(19)

Download hard_parameters.mw

Grid with numnodes option does not create files...

Asked by: nm 11353

January 28 2025

1 5

I've been evaluating Grid but I found some problems with SQLite DB when not using numnodes.

So I am now using numnodes option to setup explicitly number of nodes to use with Grid.

But the problem is now print() do not show on the screen from node code. So hard to debug. So I changed code to send debug messages to print files.

But now I find that the files do even get created when using numnodes.

When removing numnodes option, the text file gets created.

I am using FileTools:-Text:-WriteString() and FileTools:-Text:-Close() in the node code.
I also tried using fopen(). Both do not work.

Same code works OK if I do not use numnodes.

Any idea why the file do not get created when using numnodes? Worksheet to produce this is below.

I use C:\\tmp folder for testing. Feel free to change this. When I run the code and look in the folder, I do not see the text file there when using numnodes.

It is possible the file is created but saved somewhere else on the system even though the full file name is given?

It seems to me now that when using numnodes option, there are some things that work and some things that do not work. I do not know if this is by design or a bug. Any one knows?

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restart;

>	interface(version);

>	Physics:-Version();

Why task running on node do not create text file?

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restart;

>	currentdir("C:\\TMP"): #change as needed

>	foo:=proc(n::integer) local file_name::string; currentdir("C:\\TMP"): #change as needed file_name:=cat(currentdir(),"\\",n,"_file.txt"); FileTools:-Text:-WriteString(file_name,cat("processing at node =",n)); FileTools:-Text:-Close(file_name); end proc:

>	Grid:-Set(foo): Grid:-Setup("local",numnodes=1); Grid:-Run(0,foo,[0]): Grid:-Wait();

>	#No file "0_file.txt" is created in my C:\\TMP\ folder

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Another version using fopen instead of FileTools. This also do not work

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restart;

>	currentdir("C:\\TMP"): #change as needed

>

foo:=proc(n::integer)
   local file_name::string, fileID;
   currentdir("C:\\TMP"): #change as needed
   file_name:=cat(currentdir(),"\\",n,"_file.txt");
   try
        fileID := fopen(file_name,WRITE);
    catch:
        error StringTools:-FormatMessage(lastexception[2..-1]);
    end try;

   fprintf(fileID,"%s",cat("processing at node =",n));
   fclose(fileID);
end proc:

>	Grid:-Set(foo): Grid:-Setup("local",numnodes=1); Grid:-Run(0,foo,[0]): Grid:-Wait();

Download grid_question_jan_29_2025.mw

To see the file 0_file.txt get created in the folder, simply remove the numnodes option.

single PDE solver error ...

Asked by: sarah_r21 5

January 26 2025

1 2

Dear all,

I'm a new maple user trying to solve a single PDE in maple using finite volume.

For simplicity I'm using three volumes. When I'm trying to apply a simple flux limiter, up-wind scheme, (relation between the wall and the node values u[j+0.5](t)=u[j](t)), I'm solver works well and produces accurate results.

However, when I try to a more complicated flux limiter, the solver doesn't initialize and I'm getting an error:
"Error, (in dsolve/numeric/DAE/make_proc) specified dependent variables [u[0](t), u[.5](t), u[1](t), u[1.5](t), u[2](t), u[2.5](t), u[3](t), u[3.5](t), u[4](t)] do not agree with input system {u[0], u[1], u[2], u[3], u[4], u[1/2], u[1.5], u[2.5], u[3.5]}, differences: {u[1/2]}, {u[.5]}".

I would greatly appreciate it if somebody helps me on in this issue.

error.mw

How can fix `[Length of output exceeds limit of 10...

Asked by: salim-barzani 1550

January 26 2025

1 4

in a lot of my equation i have such problem and really i don't know how fix this also i try to put : in end and sometime is work and i keep contionues but sometime not there is any way for solve this problem?

limit.mw

How can define this series for generate a functio...

Asked by: salim-barzani 1550

January 26 2025

1 5

i don't know how generate this series and when i have a lot series which i can't make them automatically i don't know how write and replacing some structure like mu is zero or 1 as shown in picture can any one give me a hand?

both of them are same with little different

How remove this Error, (in Utilities:-RecognizeCyc...

Asked by: salim-barzani 1550

January 25 2025

1 4

i need find parameter in explicite way without Rootof() so i need use code of explicite but i get error but when i use all parameter without explicite all parameter come out so why i get this error?

zero.mw

Customized Key Bindings?...

Asked by: studentX369 30

January 25 2025

2 6

It's 2024 and this is still something that doesn't exist? I'd just like to swap the Enter/Shfit+Enter behaviors since I find myself writing a lot of multi-line and custom procs and boy howdy it'd be nice if I could make Maple behave at least the littllest bit like, I dunno, every other product I own and use.

NODEMaple v1.1.0 released

by: Anthrazit 885 Product: Maple 2024

January 25 2025

0 1

Just around a month after the first release I am glad to announce the second public release of this project.

Changes from last release:

added angled cuts to beam ends
fixed bug for bolt connections with thick steel plates
rewrite check if fasteners are placed within beams
removed some obsolete procedures in NODEFunctions
minor changes in XML file headers

For more information see https://github.com/Anthrazit68/NODEMaple.

Why my out come is different by same method and sa...

Asked by: salim-barzani 1550

January 25 2025

0 0

i found solution of PDE but there is some different from my solution and paper solution so there is must be a mistake becuase he solved by maple too he mentioned in the paper i try to figure out but i can't see any mistake from my solution can anyone watch where i did mistake, i change some letter in finding parameter but they are same like p=k&h=A&n=p&w=n

here is paper solution

parameter-different.mw

How do i plot the midpoint and distance?...

Asked by: paulmcquad 105

January 24 2025

1 3

I was trying to look for an easy way to plot the locations of the distance and midpoint on a graph. I found how to get the distance and midpoint functions but plotting them is hard.

Thanks in advance.