A numerical Haar wavelet-finite difference hybrid method for linear and non-linear Schrödinger equation

In this research work, we proposed a Haar wavelet collocation method (HWCM) for numerical solution of linear and nonlinear Schrödinger equations. The nonlinear term present in the model equation is linearized by a linearization technique. The Time derivative in the Schrödinger equation is approximated by forward Euler difference formula while the space derivatives are approximated by Haar function, which convert the model equation into system of algebraic equation. The stability analysis of the HWCM is also given. Several test problems are presented to verify the accuracy, stability and capability of the proposed method.