Hello,

I noticed that the Linearly Implicit Euler method (also known as the Semi-Implicit Euler method) is not available in Maple's built-in ODE solvers. This method is useful for stiff ODEs, where part of the function is treated implicitly (for the linear term) and part is treated explicitly (for the non-linear term).

I know that the Linearly Implicit Euler method is a specialized method that probably does not find enough widespread use to justify its inclusion as a standard feature in Maple, especially given Maple's focus on numerical methods such as Runge-Kutta methods and fully implicit methods for rigid equations.

I’m wondering:

1. Why isn’t this method included in Maple’s standard set of numerical solvers?
2. How can I implement this method in my own code in Maple to solve stiff ODEs?

Any guidance or examples of implementation would be greatly appreciated!

Thank you!

Linearly_Implicit_Method.pdf

The usual ODE must be solved:
y´´*(y^3-y)+y´^2 *(y^2+1)=0
"Dangerous places" of the definition domain must be described: Where are the general solution y(x) and its derivatives continuous?

Could anyone help me to convert a code written in Mathematica to a Maple worksheet? I have PDF only. Could any one have a look on Mpale sheet and PDF....

Mathematica__to_Maple.mw

Mathematica_file.pdf

An animation only allows one time parameter.

I have an setup in which I have a time parameter + another parameter or more(e.g., offset, scale, whatever).

I would like some way to easily traverse phase space and see the result and animate with time at those specific parameters(ideally animate along any path in the phase space).

In my case what this means is that there is a 2D rectangle in which represents the phase space. E.g., time x offset. This effects the animation by setting the current parameters. If the animation is animated in time it moves across the vertical. Basically a "2d slider". Alternatively have actually 2(or more) independent sliders.

Currently I have to manually set the parameter then re-execute the animation to see the new animation.

e.g.,

  animation(plot, [f(t,offset)], t=0..1,offset=1..5)

How to use maple to compute the solution of two coupling equations that both have higher order derivatives? I used dsolve and couldn't solve it.

question928.mw

I was wondering if there is a way to measure/extract the contact forces that occur during a contact event? Preferably I would like to visualize the contact forces in the 3D result view.

I would also like to extract information about slippage in a contact.

Is this somehow possible?

On my journey of discovery in the Maple world, which is new to me, I have now looked at the linear algebra packages. I am less interested in numerics than in symbolic calculations using matrices. I would like to illustrate this with the following task:

Let A be any regular (n; n) matrix over the real numbers for natural n. The regular (n; n) matrix X that solves the equation

X - A^(-1)*X*A = 0 for each A is to be determined. In this, A^(-1) is the inverse of A. Is there perhaps a symbolic solution for a specifically chosen n?

The solution to this old exercise is known. X is every real multiple of the unit/identity matrix, i.e. the main diagonal is occupied by a constant and all other matrix elements are zero.

Error.mw
As the title, I try to solve an ODE:

y(x) = (x - 1)*(x - 3)*diff(y(x), x) + f((x*y(x)^2 - 4*x*y(x) + 3*x - y(x)^2 + 4*y(x) - 1)/(x - 3))
And it seems that the ODE can be solved using Lie Symmetry method. But as I choose f to be a simple exponential function, dsolve fails to give the solution. I also try the DEtools[symgen] and receive the same result.

Can anyone tell me what's the problem? Is there some internal bug?

Executing the code in ?InvertedPendulum produces an error when

sysLin := Linearize(convert(sysEqs, list), [u(t)], [x(t), theta(t)], lin_point)

is executed. The problem is the line where EQ4 is assigned a value.

Something is wrong with the line where EQ4 is assigned a value. It is not executed.
It is like the mode changes to text for that line????

I thought I had post with collection showing timelimit still hangs in Maple. But can't find it searching. I wanted to add this to it.

If someone finds such post, please let me know and I will append this to that post and delete this.

I just found another example where int() hangs all of Maple, using timelimit. I put timelimit of 30 seconds. After 2 hrs it is still running.

Maple 2024.1 on windows 10. This shows clearly that timelimit in Maple still does not work when It was supposed to have been fixed in Maple 2021?

For me, if there is anything that will make me stop using Maple for good, it is this timelimit issue.

Because with timelimit not working all the time, my program keeps hanging. It is not possible to do antything then. Having to keep checking if the program is still running or have hanged and restarting it is not a way to develop software.

Software that have been in development for almost 45 years now like Maple, should have figured by now how to implement timelimit that works. 

Note that, with smaller timelimit it is possible it will  not hang, because longer time limit makes it end in the code path which causes the hang. When I tried 5 seconds for example instead of 30 second, it did not hang With 30 it does. so if you try it and it does not hang, please increase the timelimit a little and it will surely hang. Just make sure to do restart each time, since Maple remembers last result.

maple's server.exe was running at full cpu also.

Download int_hangs_with_timelimit.mw

Update OCT 10, 2024

This is another example showing hang in Maple 2024.1 using timelimit. So adding it to this collection. I had large collection of such problems but not able to find it now.

I was trying to verify this solution (which could very well be wrong) on ode with IC. timelimit hangs when I added assumptions as shown. Used 10,20,30 seconds, and so on. all hang. Waited and waited. 

Does it hang on other systems? I am using Windows 10 and Maple 2024.1 with 128 GB RAM on fast CPU.

Download time_limit_hang_example_oct_10_2024.mw

I would like to officially offer $1,000 prize for any one who can solve the timelimit hanging problem in Maple. Will send you personal check of this amount if you find why it hangs and provide fix to use that I can verify works.

Hi,

I recently moved from Windows 10 to Windows 11. I am using Maple 2022.2, and I got that installed and working OK. 

I have four Maple worksheets that I have saved as tasks on Windows 10, but my OS move requires some adjustments. When I try save the modified worksheets to the default Maple help database, I get an error saying that the database is read-only. When I try to make a new database file, Maple asks if it should create it, but then I get an error that Maple can't open the new database.

Suggestions?

Thanks,

Jno.

I have the function  and derivate with respect to ν and make the change variable ν=1/t it seems it doesn’t work. I put the derivate of 1/t => -1/t² by hand  (could it be done by “dchange” the hole transformation ?)

I want to approximate the value of the integral. It seems that the solution of the equation and plot in 2 situations for low-frequency ν < 10¹⁴  and for high frequency so  when the exponential is dominated.

Thus plot the whole function E2 in the two situations. Could it be done with a series?

For value h := 6.62607015*10^(-34); c := 299792458; T := 273 + 24; k := 1.380649*10^(-23);

ec := 1.602176634*10^(-19); ν1 :=10¹² ; ν2 := 10¹⁷ ;Tq := 1.765358264*10^(-19);

Could it be merged E2 into one plot for ν = 10¹² .. 10¹⁷? 

PPh1.mw

Loop is not executing all values just considerinng 1st value of tau0 =0.3.

Also how to plot a 2D graph from the loop result

Attaching sheet with questions in the sheet:
for_loop_question_rec.mw

Dear Maple user

I want to add caption for all four graphs with a,b,c,d at the bottom centre of each graph that should be arrange in 2X2 array and the array bottom caption as Figure 6, also i want to save the output of the array graphs in desktop with jpeg format. sample graph i have uploaded.

restart:
with(plots):
A1:= plot(sin(x), x = -Pi .. Pi,title = "Graph at M^2=1",caption = "Fig a"):# This caption is at the centre bottom of first graph and the title of A1 is M*M (M^2)should be display
A2:= plot(cos(x), x = -Pi .. Pi,caption = "Fig b"):# This caption is at the centre bottom of second graph
A3 := plot3d(1.5^x*sin(y), x = -3 .. 3, y = -3 .. 3,caption = "Fig c"):# This caption is at the centre bottom of Third graph
A4 := plot3d(1.3^x*sin(y), x = -1 .. 2*Pi, y = 0 .. Pi,caption = "Fig d"):# This caption is at the centre bottom of forth graph
display(Array(1 .. 2, 1 .. 2, [[A1, A2], [A3, A4]]), aligncolumns = [1],caption = "Fig 6"):# This caption at the bottom centre of array graphs 

I cannot remember that this was an issue in Maple 6/9/11, so it must have changed later on up to 22.

The following limit fails to execute

restart;
1/(r_S^5*(_C2*r_S^4 + _C2*r_S^3 + _C2*r_S^2 + f[3](0)*r_S + f[4](0)));
limit(%, f[4](0) = infinity);

It fails to calculate the limit with result as zero.

Thanks