Chebyshev Wavelets Collocation Method for Extended Fisher Kolmogorov Equations One and Two Space Dimension

Abstract

In this study, Chebyshev wavelet collocation method has been applied to obtain approximate solution of nonlinear partial differential equations. Firstly, Chebyshev wavelets and Chebyshev wavelets collocation method have been mentioned and operational matrices of rth integration of Chebyshev wavelets are derived. Secondly, using Chebyshev wavelets collocation method, we have explained how to solve fourth order nonlinear extended Fisher Kolmogorov (EFK) equation in one and two space dimensions approximately. Nonlinear EFK equation is transformed into the linear partial differential equation by quasilinearization technique. Finally, some examples have been solved by presented method. The results have shown that present method is convergent even in the case of a small number of grid points and also results have been in a good agreement with the results in literature. © 2021, This is a U.S. government work and not under copyright protection in the U.S.; foreign copyright protection may apply.