Gegenbauer wavelet collocation method for the extended Fisher-Kolmogorov equation in two dimensions

Abstract

Gegenbauer wavelets operational matrices play an important role in the numeric solution of differential equations. In this study, operational matrices of rth integration of Gegenbauer wavelets are derived and used to obtain an approximate solution of the nonlinear extended Fisher-Kolmogorov (EFK) equation in two-space dimension. Nonlinear EFK equation is converted into the linear partial differential equation by quasilinearization technique. Numerical examples have shown that present method is convergent even in the case of a small number of grid points. The results of the presented method are in a good agreement with the results in literature. © 2020 John Wiley & Sons, Ltd.