A comparison of basis functions for the pseudo-spectral method for a model reaction-diffusion problem

摘要

Different types of basis functions are considered for the pseudospectral method applied to the equation ut=Δu+ƒ(u) in 1- and 2-space dimensions. For large N, where N is the number of basis functions, the choice of Cheybyshev polynomials gives much greater accuracy than the eigenfunctions of the Laplacian Δ. However for small N (≲ 7), the eigenfunction expansion can be more accurate even with weakly nonperiodic boundary conditions.