Wavelet Solution of a Class of Nonlinear Boundary Value Problems

Abstract

As an extension to a recently developed modified wavelet Galerkin method (Commun. Nonlinear Sci. Numer. Simulat., 18(8): 1939–1948, 2013) for solving a class of nonlinear boundary value problems, especially the second order Bratu-type differential equations, in this study, we systematically investigate the convergence rate and computational accuracy of such type of problems under various differential orders. Results demonstrate that this wavelet method is very effective and accurate not only for solving second-order but also for high-order strong nonlinear differential equations.