Wavelet Galerkin Method for the Solution of Nonlinear Klein-Gordon Equations By Using B-Spline Wavelets

摘要

This paper aims to obtain approximate solutions of the one-dimensional nonlinear Klein-Gordon equation by employing Cubic B-spline wavelets. Our scheme uses the Galerkin method and approximates the solution in the terms of cubic B-spline scaling and wavelet functions. These wavelets are applied as testing and weighting functions. Because of some properties of these wavelets such as having compact support, vanishing moments and semiorthogonality, operational matrices of these wavelets are very sparse, so implementation of the method is simple and the computational time is low. The results of numerical experiments are presented for showing the accuracy of the method.