A meshfree approach for analysis and computational modeling of non-linear Schrödinger equation

Abstract

In this article, the authors proposed a meshfree approach for simulation of non-linear Schrodinger equation with constant and variable coefficients. Schrodinger equation is a classical field equation whose principal applications are to the propagation of light in non-linear optical fibers and planar waveguides and in quantum mechanics. First of all, spatial derivatives are discretized by using local radial basis functions based on differential quadrature method (LRBF-DQM) and, subsequently, the obtained system of non-linear ordinary differential equations (ODEs) is solved by fourth-order Runge–Kutta (RK-4). The stability analysis of the proposed approach is discussed by the matrix method. Numerical experiments ensure that the proposed approach is accurate and computationally efficient.