Numerical analysis for coupled systems of two-dimensional time-space fractional Schrödinger equations with trapping potentials

Abstract

In this study general and classical coupled systems of nonlinear time-space fractional Schrödinger equations (TSFSDE) with trapping potentials are investigated with a numerical approach. Theorems on stability of the finite difference schemes for such problems are established and presented with their proofs. Numerical solutions are investigated for one and two-dimensional cases. Convergence rates are proved by numerical experiments. Effect of a trapping potential on such systems is searched throughout the paper.