Numerical Solution of Nonlinear Klein-Gordon Equation Using Polynomial Wavelets

摘要

The main aim of this paper is to apply the polynomial wavelets for the numerical solution of nonlinear Klein-Gordon equation. Polynomial scaling and wavelet functions are rarely used in the contexts of numerical computation. A numerical technique for the solution of nonlinear Klein-Gordon equation is presented. Our approach consists of finite difference formula combined with the collocation method, which uses the polynomial wavelets. Using the operational matrix of derivative, we reduce the problem to a set of algebraic equations by expanding the approximate solution in terms of polynomial wavelets with unknown coefficients. An estimation of error bound for this method is investigated. Some illustrative examples are included to demonstrate the validity and applicability of the approach.