Legendre Wavelet Quasilinearization Method for Nonlinear Klein-Gordon Equation with Initial Conditions

Abstract

A new numerical method using Legendre wavelet together with the quasilinearization for solving nonlinear Klein-Gordon equation with initial conditions is proposed. In the proposed scheme both time as well as spatial derivatives of the Klein Gordon equation are approximated using wavelet without the help of Laplace transform, a contrast to the schemes available in the recent literature. Numerical studies assure that the less number of grid points are required to produce better accuracy and more stable with faster convergence than the Laplace transform based Legendre wavelet method. Further, While solving them numerically in the last section, a comparison is provided between Python and Matlab. The order of accuracy in Python and Matlab are same but Python takes much lesser time to produce the output compared to Matlab [Table 5].