An implicit pseudospectral scheme to solve propagating fronts in reaction‐diffusion equations

Abstract

Some Reaction‐Diffusion equations present solutions of the traveling wave form. In this work, we present an implicit numerical scheme based on finite difference originally proposed to solve hyperbolic equations. Then, this method is improved using a pseudospectral approach to discretize the spatial variable. The results prove that this new scheme is useful to solve equations of the parabolic type which presents traveling wave solutions. In particular, problems where a reduction in the number of discretization points and an increase of the size of the time step play an important role in their solution are considered. The implicit scheme presented involves the solution of linear systems only. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 86–105, 2016

Finite element analysis and approximation of Burgers’‐Fisher equation

“…For example, Adomian decomposition method (ADM) , homotopy analysis method (HAM) , homotopy perturbation method (HPM) , variation iteration method (VIM) , tanh‐coth method , Exp‐function method , and so on. are some of the analytical methods whereas Haar wavelet method , spectral collocation method , collocation method using radial basis , spectral domain decomposition approach , finite difference method , finite difference based pseudospectral approach , and so on fall in the category of numerical methods.…”