Laguerre wavelet solution of Bratu and Duffing equations

Abstract

The aim of this study is to solve the Bratu and Duffing equations by using the Laguerre wavelet method. The solution of these nonlinear equations is approximated by Laguerre wavelets which are defined by well known Laguerre polynomials. One of the advantages of the proposed method is that it does not require the approximation of the nonlinear term like other numerical methods. The application of the method converts the nonlinear differential equation to a system of algebraic equations. The method is tested on four examples and the solutions are compared with the analytical and other numerical solutions and it is observed that the proposed method has a better accuracy.