When solving partial differential equations (PDEs) using Fast Fourier Transforms (FFT), it's crucial to understand the implications of boundary conditions. The default behavior of FFT is to assume periodic boundary conditions, which can lead to inaccuracies if the domain is non-periodic. For non-periodic domains, utilizing discrete sine or cosine transforms can be effective depending on the specific boundary conditions. However, for a more general approach that accommodates various boundary conditions, employing a discrete Chebyshev transform is recommended, as it allows for the use of FFT-based algorithms while providing greater flexibility in handling different types of boundaries.
