A Haar wavelet collocation method for coupled nonlinear Schrödinger–KdV equations

Abstract

In this paper, to obtain accurate numerical solutions of coupled nonlinear Schrödinger–Korteweg-de Vries (KdV) equations a Haar wavelet collocation method is proposed. An explicit time stepping scheme is used for discretization of time derivatives and nonlinear terms that appeared in the equations are linearized by a linearization technique and space derivatives are discretized by Haar wavelets. In order to test the accuracy and reliability of the proposed method [Formula: see text], [Formula: see text] error norms and conserved quantities are used. Also obtained results are compared with previous ones obtained by finite element method, Crank–Nicolson method and radial basis function meshless methods. Error analysis of Haar wavelets is also given.