Mixed Shifted Generalized Laguerre–Fourier Spectral Method for Exterior Problem of Fisher Equation

ABSTRACT In this article, we investigate the mixed spectral method using the shifted generalized Laguerre functions and Fourier series for exterior problem of Fisher equation. We introduce the shifted generalized Laguerre functions and derive some related approximation results. We propose a mixed spectral scheme for the Fisher equation outside a disk and prove the generalized stability and the convergence of the developed method. Numerical results demonstrate the spectral accuracy in space.