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Trouble Plotting Solution in Maple Using Fokas Met...

Asked by: Paras31 240
integration pde numeric
3 hours ago
1  1

Hello,

I’m trying to solve a problem from Modern Mathematical Methods for Scientists and Engineers using Maple, specifically applying the Fokas method (Unified Transform) to the heat equation on the half-line. The problem setup matches Example 9.1 from the book.

Everything runs fine until I try to plot the solution using plot3d.
 

> 

restart; with(plots); with(LinearAlgebra); with(Student[VectorCalculus]); V := proc (k, x, t) options operator, arrow; -((1/2)*I)*exp(I*k*x-k^2*t)*(1/(k-I)+1/(k+I)-k*(1/(k^2+1)+1/(k^2-1)))/(Pi*k) end proc

proc (k, x, t) options operator, arrow; Student:-VectorCalculus:-`-`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(I, Student:-VectorCalculus:-`*`(2, Pi)^Student:-VectorCalculus:-`-`(1)), Student:-VectorCalculus:-`*`(exp(Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`*`(Student:-VectorCalculus:-`*`(I, k), x), Student:-VectorCalculus:-`-`(Student:-VectorCalculus:-`*`(k^2, t)))), k^Student:-VectorCalculus:-`-`(1))), Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`+`(k, Student:-VectorCalculus:-`-`(I))^Student:-VectorCalculus:-`-`(1), Student:-VectorCalculus:-`+`(k, I)^Student:-VectorCalculus:-`-`(1)), Student:-VectorCalculus:-`-`(Student:-VectorCalculus:-`*`(k, Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`+`(k^2, 1)^Student:-VectorCalculus:-`-`(1), Student:-VectorCalculus:-`+`(k^2, -1)^Student:-VectorCalculus:-`-`(1))))))) end proc

 (1)
> 

phi1 := (1/8)*Pi; phi2 := 7*Pi*(1/8); k1 := proc (r) options operator, arrow; r*exp(I*phi1) end proc; k2 := proc (r) options operator, arrow; r*exp(I*phi2) end proc; dk1 := proc (r) options operator, arrow; diff(k1(r), r) end proc; dk2 := proc (r) options operator, arrow; diff(k2(r), r) end proc
> 

u1 := proc (x, t) options operator, arrow; evalf(int(Re(V(k1(r), x, t)*dk1(r)-V(k2(r), x, t)*dk2(r)), r = 0 .. 80)) end proc

proc (x, t) options operator, arrow; evalf(Student:-VectorCalculus:-int(Re(Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`*`(V(k1(r), x, t), dk1(r)), Student:-VectorCalculus:-`-`(Student:-VectorCalculus:-`*`(V(k2(r), x, t), dk2(r))))), r = 0 .. 80)) end proc

 (2)
> 

u := proc (x, t) options operator, arrow; exp(-x/sqrt(2))*cos(t-x/sqrt(2))+u1(x, t) end proc

proc (x, t) options operator, arrow; Student:-VectorCalculus:-`+`(Student:-VectorCalculus:-`*`(exp(Student:-VectorCalculus:-`-`(Student:-VectorCalculus:-`*`(x, sqrt(2)^Student:-VectorCalculus:-`-`(1)))), cos(Student:-VectorCalculus:-`+`(t, Student:-VectorCalculus:-`-`(Student:-VectorCalculus:-`*`(x, sqrt(2)^Student:-VectorCalculus:-`-`(1)))))), u1(x, t)) end proc

 (3)
> 

plot3d(u(x, t), x = 0 .. 3, t = 0 .. 2*Pi, axes = boxed, shading = zhue, style = surface, labels = ["x", "t", "u(x,t)"])
> 

NULL


 

Download fokas_method.mw

Has anyone successfully handled similar integrals inside plot3d? Is there a better way to numerically evaluate the Fokas integral so Maple can plot it efficiently?

 

Where is the "Stop Execution" icon?...

Asked by: WD0HHU 40
interrupt gui duplicate-question
June 17 2025
0  1

Maple 2024 had a very well defined "Stop Execution" symbol on the desktop.  

Maple 2025 doesn't have an obvious symbol somewhere.  Also, the two little "dots" that I once had in the lower left bottom in Maple 2025 have disappeared! There is only a bar at the bottom which seems to do nothing.

is this a weakness in simplify?...

Asked by: nm 11353
simplify simplification trig
June 04 2025
0  2

Wondering what the experts here think of this. Should not simplify have worked on this automatically? By trial and error, found that combine command is what simplified it the best.

But I think simplify should also have done the same.  

Interested to hear what others think, and why simplify (even using trig option) did not do it.   

The issue is that this is done in code, without lookin at the screen and deciding what to do based on what the expression "looks like".

> 

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

> 

A:=(((sin(sqrt(3)/2)*sqrt(3) - 3*cos(sqrt(3)/2))*cos(sqrt(3)*x/2) - sin(sqrt(3)*x/2)*(sqrt(3)*cos(sqrt(3)/2) + 3*sin(sqrt(3)/2)))*exp(-1/2 + x/2))/3 ;

(1/3)*((sin((1/2)*3^(1/2))*3^(1/2)-3*cos((1/2)*3^(1/2)))*cos((1/2)*3^(1/2)*x)-sin((1/2)*3^(1/2)*x)*(3^(1/2)*cos((1/2)*3^(1/2))+3*sin((1/2)*3^(1/2))))*exp(-1/2+(1/2)*x)

> 

B:=- exp(-1/2 + x/2)*(sqrt(3)*sin(sqrt(3)*(x - 1)/2) + 3*cos(sqrt(3)*(x - 1)/2))/3;

-(1/3)*exp(-1/2+(1/2)*x)*(3^(1/2)*sin((1/2)*3^(1/2)*(x-1))+3*cos((1/2)*3^(1/2)*(x-1)))

> 

simplify(A-B); #show these are same

0

> 

simplify(A,trig)

-(1/3)*((-sin((1/2)*3^(1/2))*3^(1/2)+3*cos((1/2)*3^(1/2)))*cos((1/2)*3^(1/2)*x)+sin((1/2)*3^(1/2)*x)*(3^(1/2)*cos((1/2)*3^(1/2))+3*sin((1/2)*3^(1/2))))*exp(-1/2+(1/2)*x)

> 

simplify(A)

-(1/3)*((-sin((1/2)*3^(1/2))*3^(1/2)+3*cos((1/2)*3^(1/2)))*cos((1/2)*3^(1/2)*x)+sin((1/2)*3^(1/2)*x)*(3^(1/2)*cos((1/2)*3^(1/2))+3*sin((1/2)*3^(1/2))))*exp(-1/2+(1/2)*x)

> 

simplify(A,size)

-(1/3)*((-sin((1/2)*3^(1/2))*3^(1/2)+3*cos((1/2)*3^(1/2)))*cos((1/2)*3^(1/2)*x)+sin((1/2)*3^(1/2)*x)*(3^(1/2)*cos((1/2)*3^(1/2))+3*sin((1/2)*3^(1/2))))*exp(-1/2+(1/2)*x)

> 

simplify(normal(A))

-(1/3)*((-sin((1/2)*3^(1/2))*3^(1/2)+3*cos((1/2)*3^(1/2)))*cos((1/2)*3^(1/2)*x)+sin((1/2)*3^(1/2)*x)*(3^(1/2)*cos((1/2)*3^(1/2))+3*sin((1/2)*3^(1/2))))*exp(-1/2+(1/2)*x)

> 

combine(A); #finally

(-(1/3)*3^(1/2)*sin((1/2)*3^(1/2)*(x-1))-cos((1/2)*3^(1/2)*(x-1)))*exp(-1/2+(1/2)*x)

 

 

Download simplify_vs_combine_june_4_2025.mw

solve failing on second time called....

Asked by: nm 11353
solve assuming physics
May 28 2025
2  4

I've been debugging this for 20 hrs and finally able to make an example.

I noticed that solve() suddenly no longer works and times out.

First time calling solve() works. Second time it I see message

               Warning, solve may be ignoring assumptions on the input variables.

And it hangs.  Same exact code.   It has to do with calling odetest before and using Physics:-Setup('assumingusesAssume' = false):

i.e. this works
  
     odetest(...) assuming integer
     solve(....) #no hang
     odetest(....) assuming positive

     odetest(...)  assuming integer
     solve(....)  #no hang

But this does not work

     odetest(...) assuming integer
     solve(....) #no hang
     Physics:-Setup('assumingusesAssume' = false):
     odetest(....) assuming positive
     Physics:-Setup('assumingusesAssume' = true):
     odetest(...) assuming integer
     solve(...)   #HANGS     

Here is worksheet showing the problem. If I remove first call to odetest, solve do not hang.

Also removing Physics:-Setup('assumingusesAssume' = false):, solve also works OK. (ie. does not hang)

So it has to do with some internal caching which causes solve to stop working.

Can others reproduce this and can cause it and how to fix it so solve do not hang second time?

The input used below is not important. It is just what I found to cause this. One would expect solve() to work same way for same input all the time.

Also, same problem happens when using PDEtools:-Solve instead of solve. It hangs second time.

> 

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1873 and is the same as the version installed in this computer, created 2025, May 18, 21:44 hours Pacific Time.`

> 

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 20 and is the same as the version installed in this computer, created May 23, 2025, 23:34 hours Eastern Time.`

> 

restart

DEFINE input

 
> 

ode:=y(x)*sqrt(1 + diff(y(x), x)^2) - a*y(x)*diff(y(x), x) - a*x = 0:
sol:=-_C4^2 + (-y(x)*sqrt(_C4^2/y(x)^2) + a*x)^2/a^2 + y(x)^2 = 0:
ode_to_test:=y(x)*(1+diff(y(x),x)^2)^(1/2)-a*y(x)*diff(y(x),x)-a*x = 0:

FIRST TIME solve works

 
> 

    try
        timelimit(30,(odetest(sol,ode,y(x)) assuming integer));
    catch:
        NULL;
    end try:

    try
        timelimit(30,[solve(ode_to_test,diff(y(x),x))]);
        print("SOLVE worked");              
    catch:
        print("WHY TIMED OUT??");              
    end try:

    Physics:-Setup('assumingusesAssume' = false):
    try
        timelimit(30, (odetest(sol,ode,y(x)) assuming positive) );
    catch:
        NULL;
    end try:
    Physics:-Setup('assumingusesAssume' = true):

"SOLVE worked"

> 

 

> 

 

RUN SAME CODE AS ABOVE again, now it does not work

 
> 

    try
        timelimit(30,(odetest(sol,ode,y(x)) assuming integer));
    catch:
        NULL;
    end try:

    try
        timelimit(30,[solve(ode_to_test,diff(y(x),x))]);
        print("SOLVE worked");              
    catch:
        print("WHY TIMED OUT??");              
    end try:

    Physics:-Setup('assumingusesAssume' = false):
    try
        timelimit(30, (odetest(sol,ode,y(x)) assuming positive) );
    catch:
        NULL;
    end try:
    Physics:-Setup('assumingusesAssume' = true):

Warning, solve may be ignoring assumptions on the input variables.

"WHY TIMED OUT??"

 

 

 

 

Download why_solve_stops_working_maple_2025_may_28_2025.mw

This worksheet below shows that by removing Physics:-Setup('assumingusesAssume' = false): now solve works OK second time. (I turn on/off Physics:-Setup('assumingusesAssume' since I found sometimes it can help with odetest to turn it off in some other cases. But now I am scared of touching this setting as it seems to have side effects internally)

> 

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1873 and is the same as the version installed in this computer, created 2025, May 18, 21:44 hours Pacific Time.`

> 

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 20 and is the same as the version installed in this computer, created May 23, 2025, 23:34 hours Eastern Time.`

> 

restart

DEFINE input

 
> 

ode:=y(x)*sqrt(1 + diff(y(x), x)^2) - a*y(x)*diff(y(x), x) - a*x = 0:
sol:=-_C4^2 + (-y(x)*sqrt(_C4^2/y(x)^2) + a*x)^2/a^2 + y(x)^2 = 0:
ode_to_test:=y(x)*(1+diff(y(x),x)^2)^(1/2)-a*y(x)*diff(y(x),x)-a*x = 0:

FIRST TIME solve works

 
> 

    try
        timelimit(30,(odetest(sol,ode,y(x)) assuming integer));
    catch:
        NULL;
    end try:

    try
        timelimit(30,[solve(ode_to_test,diff(y(x),x))]);
        print("SOLVE worked");              
    catch:
        print("WHY TIMED OUT??");              
    end try:

    try
        timelimit(30, (odetest(sol,ode,y(x)) assuming positive) );
    catch:
        NULL;
    end try:

"SOLVE worked"

> 

 

> 

 

RUN SAME CODE AS ABOVE again, now it does not work

 
> 

    try
        timelimit(30,(odetest(sol,ode,y(x)) assuming integer));
    catch:
        NULL;
    end try:

    try
        timelimit(30,[solve(ode_to_test,diff(y(x),x))]);
        print("SOLVE worked");              
    catch:
        print("WHY TIMED OUT??");              
    end try:

    try
        timelimit(30, (odetest(sol,ode,y(x)) assuming positive) );
    catch:
        NULL;
    end try:

"SOLVE worked"

 

 

 

 

Download why_solve_stops_working_maple_2025_may_28_2025_V2.mw

How to find what changed in SupportTools after eac...

Asked by: nm 11353
update supporttools
May 06 2025
4  1

I asked similar question 5 years ago about Physics update but it was not possible to find this information

How-To-Find-What-Changed-In-Physics

I'd like to ask now again same about  SupportTools. Can one find out what update is actually included in new version?

Even if it is just 2-3 lines. It will be good if users had an idea what was fixed or improved in the new version.

Any update to software should inlcude such information. Not asking for details, just general information will be nice. Right now one does an update and have no idea at all what the new update fixed or improved which is not good.

May be such information can be displayed on screen after a user updates?

why some help pages are empty?...

Asked by: nm 11353
documentation
May 01 2025
3  1

This happens in Maple 2025, but when I checked Maple 2024.2, same thing happen.

To reproduce, I typed ?coeff in the worksheet. Now the help page for coeff comes up OK. On the right, there are some links below "see also". 

Clicking on the one that says PolynomialTools[CoefficientVector] and now an EMPTY page opens up.

Also, typing ?PolynomialTools in worksheet, opens the help page for Overview of the PolynomialTools Package. Now clicking on CoefficientList link, opens an EMPTY page. Same when clicking on CoefficientVector, an EMPTY page !

Have not checked all the links in the help page, but why are some commands have empty help pages?

 

 

Some questions about MapleCloud ...

Asked by: C_R 3402
browser gui
April 24 2025
0  2

MapleCloud opend from Maple2025 and 2024.

Has this extended scrollbar always been like this?
Maybe it is a browser thing.
Which browser is Maple using?
Are there any settings I could adjust?

where is Maple's help page for Abel second kin...

Asked by: nm 11353
April 15 2025
3  1

I can't find the help page for Abel second kind, class B. 

Maple has help page for Abel second kind, class A and Abel second kind, class C. But not for class B. 

Here is an example of Abel second kind class B

ode:=(3*t*y(t)+y(t)^2)+(t^2+t*y(t))*diff(y(t),t)=0;
DEtools:-odeadvisor(ode)

I wanted to know the difference and the transformation used for class B to make it Abel first kind.

I googled and can't find it. Also local help skips over class B.

Is this documented somewhere else?

btw, find error on the help page for class A. Transformation used is wrong. Will leave this for another question.

Strange rendering of assignement operator: Has som...

Asked by: C_R 3402
April 14 2025
3  6

I have repeatedly seen this on two Windows PCs:

The assignement operator := is rendered as a roman d

This happens after using Maple for some time.
 Exiting Maple and restart of Maple is required. Has someone noticed the same?
All on Windows 10 and for sure in screen reader mode (my default, cannot report on the new GUI).

Ribbon interface ......

Asked by: vv 13785
April 14 2025
2  3

It seems that the new Ribbon interface has several bugs (probably an update will come soon). So, not only the Export As is not working, but I see that (at least in Windows), opening a worksheet with a large output will display the output using the Maple input font.
Just save a .mw with the content:

expand((x+1)^200);

and then open it.

Magnification in Maple worksheets and help pages...

Asked by: Jean-Michel 40
April 13 2025
2  4

hello everyone,

I am a bit shortsighted even with my glasses.

So my question is easy :: is there a way that when I open a (new) worksheet the magnification is 150%.

I can do it easily by hand but I am looking for 'something' in my maple.ini file to do this?

As well with the help pages.

Because even if I have a 150% magnification and I call a help page the display is still 100 % not 150%.

A part that I would like to set for every session a Digits:16 .

In the .ini file where I must input this? A ";" or not?

Thank you veru much.

Jean-Michel

Export As, Save As...

Asked by: vv 13785
export gui save
April 10 2025
3  4

In the File menu,  the Export As dialog is missing. Only the default (.pdf) can be used; no .mpl or .tex)
The Save As dialog is incomplete (e.g. save to .mws).

Or, is the installation corrupted?

Display quality with rotated screens...

Asked by: Anthrazit 885
resolution java orientation
April 09 2025
3  13

I need to take up an issue which is quite old, but still unsolved.

https://www.mapleprimes.com/questions/234249-Text-Quality-On-Screen

The problem is that in specific display configurations with one (rotated) vertical screen and multiple horizontal screens, the quality of fonts especially is significantly lower in Maple as with a configuration with just horizontal screens.

The affect is visible in Maple when it is on the horizontal (unrotated) screens.

Here are screenshots for comparision, and the layout of my desktop.

Screen layout:

Screenshot rotated

Screenshot unrotated

It seems that the problem is present when starting Maple. Changing the rotation of the screen when Maple is running does not affect the font quality in Maple.

Other (Windows) programs are not affected at all of this changes, so this seems to be a Java issue.

Open file dialog: How to list only Maple files...

Asked by: C_R 3402
gui
April 07 2025
2  3

With the new GUI:
I get all files (*.*) listed by default.
Other file types to filter are not listed.

Is this the same on other machines?

Can I do something about it?

Document layout / tab indenting...

Asked by: Anthrazit 885
April 07 2025
0  1

How do I make indents in Maple 2025 for more readable layout?

Haven't used that much in 2024, but according to help this should be in Format - Tab settings. I don't find that in 2025 unfortunately.

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