Solving an Equation with the SSFM Method - John's Urgent Question

[Johnbasko]

hello all
Im trying to solve the equation:

i*dV/dt = d^2V/dz^2 + V*sqrt(1-V^2)

I want to try by the split step Fourier method.

My problem is that most of the code/solvers I saw that implement the SSFM method are when the evolution is in space not in time, meaning the first derivative is d/dz and the second is (d/dt)^2

any idea how it fact or maybe it doesn't matter ?

furthermore, you think it is possible to solve itusing the MATLAB solver for PDE ?
thanks in advance
John.

 

[Mute]

In your equation, replace z with t and t with z:

i*dV/dz = d^2V/dt^2 + V*sqrt(1-V^2)

Is this the form you require to use the split-step method? If so, all I've done is a cosmetic change; time is now labeled by z and space is now labeled by t. So, it looks like the method should work with your equation based on what you've said.

 

[Johnbasko]

Mute, thank you for the response.

Ofcourse, I understand this cosmetic changed, and indeed, by this change the form is regular.
But, I wonder if it's is allow, I mean if this changed might influence on the result of the SSFM method i will use in this equation ?
or the result should be okay ?

In all the material I've looked I've noticed that always the evolution (i.e: the first derivative) if on the space (Z domain), so infact my question whether this cosmetic change might harm the result or all should be the same ?
Thanks

p.s: Furthermore, I would like to know if anyone know an organized source code for the SSFM ?

 

[Mute]

It shouldn't make any difference. The label t for time or z for space is just a convenience to us; the computer doesn't know that 'z' is space or 't' is time. You're the one who decides how to interpret the labels, so you can freely interpret z as time. So, if you make that cosmetic change and run the program, all you have to do is interpret the output properly, remembering that after the cosmetic change time is now z and space is now t.

 

[blue_raver22]

Hello John,

Thank you for reaching out with your question about solving an equation using the split step Fourier method (SSFM). The SSFM is a numerical method commonly used for solving partial differential equations (PDEs) in physics and engineering. It is a powerful tool that can handle complex equations and boundary conditions.

Based on your equation, it seems like you are trying to solve a PDE in both space and time. The SSFM method is typically used for solving PDEs in space, but it can also be adapted for time-dependent problems. However, the implementation may differ from the traditional SSFM approach.

I would recommend looking into literature or consulting with experts in the field to see if there are any specific adaptations or modifications needed for using SSFM for time-dependent PDEs. It is possible that the code or solver you have seen may need to be modified for your specific equation.

As for using MATLAB's solver for PDEs, it is definitely possible. MATLAB has built-in functions for solving PDEs, including the SSFM method. However, it is important to carefully consider the capabilities and limitations of the solver and ensure that it is suitable for your specific equation.

I hope this helps and good luck with your research!

Best,