Numerical analysis of linear and non-linear dispersive equation using Haar scale-3 wavelet

Abstract

The focus of the current study is to propose a numerical technique based upon the Scale-3 Haar wavelets for the solution of the linear and non-linear dispersive equation. In this scheme, spatial and time discretization is done by using two-dimensional Haar scale 3 wavelets and the quasi-linearization technique is used to linearize the non-linear term present in the non-linear dispersive equations. The collocation method is used with Haar scale 3 wavelets to convert the dispersive differential equation into the system of algebraic equations which are further solved with the help of the Thomas algorithm. The established method is tested on three equations and compared with already existing results in the literature to establish the competency of the proposed scheme.