Numerical treatments of the nonlinear coupled time‐fractional Schrödinger equations

Abstract

In this article, we focused on solving numerically the coupled nonlinear Schrödinger equations (NLFSEs) with Caputo fractional derivative in time. The discrete schemes are constructed by using the trigonometric B‐spline collocation method and the non‐polynomial B‐spline method for space discretization respectively, while the ‐formula is applied in time discretization. The Von Neumann approach is applied to examine the stability of the proposed methods. For validating the accuracy and efficiency of the presented schemes, numerical tests are compared with the exact solution.