Numerical study of nonlinear generalized Burgers–Huxley equation by multiquadric quasi-interpolation and pseudospectral method

This paper develops an efficient numerical meshless method to solve the nonlinear generalized Burgers–Huxley equation (NGB-HE). The proposed method approximates the unknown solution in the two stages. First, the θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta$$\end{document}-weighted finite difference technique is adopted to discretize the temporal dimension. Second, a combination of the multiquadric quasi-interpolation and pseudospectral (denoted by MQQI-PS) is constructed to approximate the spatial derivatives. In addition, a cross-validation technique is used to find the shape parameter value. Finally, numerical results are illustrated to show the accuracy and efficiency of the MQQI-PS method.