A localized Fourier collocation method for the numerical solution of nonlinear fractional Fisher–Kolmogorov equation

Abstract

This paper deals with a meshless method based on the localized Fourier collocation method (LFCM) combined with time discretization schemes to rigorously compute solutions for the Fisher-Kolmogorov equation. The idea is to generate the solution as the expansion of the modified Fourier series on the local subdomain and to use the reconstruction parameter to impact the accuracy and the rate of convergence. As applications, solutions of the factional Fisher-Kolmogorov equation on linear and nonlinear irregular domain are rigorously computed. Moreover, additional fourth-order terms in this model the so-called factional extended Fisher-Kolmogorov equation can be treated as a linear problem using the quasilinearization technique. Finally, we present an error analysis based on the illustration of convergence and accuracy graphs.