Limitation of Split-Step Fourier method

[iamkitchai]

Hi,

I'm using the Split-step Fourier method for programming. I am going to use this method to solve a nonlinear Schrodinger equation with variable coefficients.

But before implement this method in Matlab, I would like to ask if this method always works in all siturations, and in what cases, this method can not be used.

Thanks,
Lam

 

[libertas]

hi,
I also want to use split step Fourier method to solve gross-pitaevskii equation (nonlinear Schrodinger eq.). as well as I know it is the best method to solve this kind of equations.
But unfortunately I can't find any algorithm or a source code or something that gives a detailed information about this method. So I don't know how to implement this method.
Could you recommend me anything (paper, book, website etc.) about this? Or have you got any written code that you can send me?

Thanks,
Elif

 

[tacman]

The Split-Step Fourier method is a powerful tool for solving nonlinear Schrodinger equations with variable coefficients. However, like any numerical method, it has its limitations and may not always be applicable in every situation. Some potential limitations of the Split-Step Fourier method include:

1. Non-convergence: The Split-Step Fourier method may not converge or produce accurate results for certain types of nonlinear equations, particularly those with highly oscillatory solutions or singularities.

2. Boundary conditions: This method may not be suitable for solving equations with complicated boundary conditions, as it requires a periodic or semi-periodic domain.

3. Computational efficiency: While the Split-Step Fourier method is generally considered to be a fast and efficient method, it may become computationally expensive for large-scale problems with high-dimensional domains.

4. Applicability to other equations: This method is specifically designed for solving nonlinear Schrodinger equations and may not be suitable for other types of equations.

In summary, while the Split-Step Fourier method is a reliable and widely used method for solving nonlinear Schrodinger equations with variable coefficients, it is important to carefully consider its limitations and applicability before implementing it in your programming. It is also recommended to consult with experts in the field or conduct further research to ensure the most appropriate method is used for your specific problem.