Numerical Simulation of Nonlinear Schrödinger Equation in One and Two Dimensions

Abstract

The present study aims to develop a hybrid scheme using trigonometric cubic B-spline basis functions with differential quadrature method for solving nonlinear Schrödinger equation in both one and two dimensions. This method reduces the nonlinear equation into a set of ordinary differential equations which can be further solved by the modified form of Ruge–Kutta method. This proposed method has been applied to this equation using two different approaches and also has been tested for proficiency on seven numerical examples. The obtained numerical results found to be synonymous when related with the exact solution. The obtained numerical results are also in good agreement with the results available in the literature. Comparison of numerical and the exact solution is depicted in the form of figures and tables.