how to change time integration in pdepe

ode15s is used in pdepe. How to change it to say ode23 etc when in need?

[Torsten]

There is no need. The system of ODEs resulting from the discretization is strongly stiff and often contains algebraic equations as well. ode15s is the integrator of choice.

[feynman feynman]

But ode15s doesn't work for everything it seems to me. There're cases where ode15s reports errors but ode23 yields sth right. How can that be?

[Torsten]

Usually, "ode15s" is superior to "ode23". Thus, TMW decided to use it as the ode integrator for "pdepe". There is no way to use "ode23" within "pdepe". But you can discretize the equations on your own and use "ode23" as time integrator, if you feel the need to do so.

[feynman feynman]

right, but I can't just copy out pdepe since there're private helper functions I have no access to?

[Torsten]

I don't know how "pdepe" is arranged. If you can find the call to "ode15s" somewhere while editing the code, you could try to change it to a call to "ode23".

[feynman feynman]

not really, because in pdepe there are functions like pdentrp that we can't use out of pdepe.

Answer 1

[Sanju]

Hi feynman feynman,

I understand that you want to change ODE solver whenever required,

‘pdepe’ is a function specifically designed for solving systems of partial differential equations in MATLAB. ‘pdepe’ internally selects an appropriate ODE solver based on the characteristics of the problem, and it does not allow you to specify ‘ode23’ or any other specific ODE solver.

If you need more control over the ODE solver used within ‘pdepe’, you can try to adjust the options provided to ‘pdepe’. For instance, you can specify tolerances, time steps, and other parameters that might affect the behaviour of the internal ODE solver.

Also, there’s an option for directly selecting the desired ODE solver for which you can directly use ‘ode23’ function call to solve the ODE,

Here’s an example code you can refer to,

% Define the ODE function
odefun = @(t, y) -y;

% Define the initial condition
y0 = 1;

% Define the time span
tspan = [0 10];

% Solve the ODE using ode23
[t, y] = ode23(odefun, tspan, y0);

Similarly, you can use other ODE solvers available in MATLAB such as ode45, ode23s, etc., by replacing ode23 with the desired solver function handle.

You can also refer to the following documentation links if required,

https://www.mathworks.com/help/matlab/ref/pdepe.html

https://www.mathworks.com/help/matlab/math/choose-an-ode-solver.html

https://www.mathworks.com/help/matlab/ref/odeset.html

Hope this helps!

[feynman feynman]

Thank you but the code you pasted can't be embedded into pdepe can it?

[Torsten]

But you know now how to change the time integrator, don't you ?

[feynman feynman]

yes in ODE solvers but not in pdepe.

[Torsten]

I don't understand the problem.

Load the code of pdepe and pdentrp into the editor, rename the two functions to pdepe1 and pdentrp1, save them under the new names, adapt the calls to pdentrp in pdepe1 to pdentrp1, change the ode integrator in pdepe1 to ode23s and work with pdepe1 as if it were pdepe.

[feynman feynman]

Oh sorry I thought pdentrp couldn't be visible but it actually can. I was told pdentrp was a private function and maybe that isn't true. Thank you for your tips!

[Torsten]

We already discussed this. I get the impression that you thank for suggestions, but don't read them.

[feynman feynman]

I did read them and appreciate your help with all my heart but my brain wasn't working properly yesterday sorry

[feynman feynman]

@Torsten pdentrp still defies modification of ode solvers in pdepe even when the code of pdentrp is copied out as you suggested. The following is what appears after running mypdepe even when mypdepe=pdepe.

Not enough input arguments.

Error in pdentrp (line 15)
xout = xout(:)';

Error in mypdepe (line 255)
[U,Ux] = pdentrp(m,xmesh(1),y0(:,1),xmesh(2),y0(:,2),xi(1));

[Torsten]

Read again:

Load the code of pdepe and pdentrp into the editor, rename the two functions to pdepe1 and pdentrp1, save them under the new names, adapt the calls to pdentrp in pdepe1 to pdentrp1, change the ode integrator in pdepe1 to ode23s and work with pdepe1 as if it were pdepe.

Did you copy "pdentrp" to "pdentrp1" and change the calls to this function from "pdentrp" to "pdentrp1" in "pdepe1" ? The error above is about the function "pdentrp", not "pdentrp1".

And I wonder why the first input argument "singular" to pdentrp(1) is missing.

BE CAREFUL NOT TO MAKE CHANGES TO THE ORIGINAL FUNCTIONS PDEPE AND PDENTRP, ONLY TO THE COPIES.

[feynman feynman]

Oh I didn't know why singular was gone but when I put it back to pdepe1, things work! Thank you so much and sorry for bothering you due to a mistake from me.

However, tests show that when ode15s in pdepe is replaced with any other ode solvers, there's no convergent solution. ode15s is the only one that works in pdepe.

[Torsten]

ode23t does not work ?

[feynman feynman]

Thanks yes it does! How did you know?

[Torsten]

https://uk.mathworks.com/help/matlab/math/summary-of-ode-options.html

The options for the mass matrix have to be equal to ode15s (especially the mass matrix must be allowed to be singular). ode23t is the only solver that satisfies this requirement.

[feynman feynman]

Oh yes, but why do we only need to satisfy those for the mass matrix not anything else?

[Torsten]

Because the other options are not related to the structure of the DAE problem, but to the performance of its solution.

If the solver cannot cope with the structure of the problem, this is a Ko criterion right at the beginning.

[feynman feynman]

great point thank you