Block-Hybrid method for Burgers-Huxley equation

Abstract

In this study, Lie symmetries, spectral quasilinearization method, multi-domain bi- variate spectral quasilinearization method, and block-hybrid method are utilized in solving the second order nonlinear evolution problems. The spectral quasilin- earization method is attained by applying the spectral collocation technique in space derivatives, the multi-domain bivariate spectral quasilinearization method is applied both in time and space derivatives and the block-hybrid method is applied only on the time derivatives. The applicability of these techniques is presented by solving a class of second-order nonlinear evolution PDEs, specifically the Burgers-Huxley equation, Burgers-Fisher equation, FitzHugh-Nagumo equation, and Coupled Burgers' equation. The numerical outcomes are confirmed for accuracy by comparing them with analytical solutions. Tables for the spectral quasilinearization method, multi-domain bivariate spectral quasilinearization method, and Block-Hybrid method with their computational times were produced for comparing the order of precision for each technique, and error graphs are displayed.