An efffcient numerical scheme for two-dimensional nonlinear time fractional Schrödinger equation

Abstract

In this paper, a linearized fully discrete scheme is proposed to solve the two-dimensional nonlinear time fractional Schrödinger equation with weakly singular solutions, which is constructed by using L1 scheme for Caputo fractional derivative, backward formula for the approximation of nonlinear term and five-point difference scheme in space. We rigorously prove the unconditional stability and pointwise-in-time convergence of the fully discrete scheme, which does not require any restriction on the grid ratio. Numerical results are presented to verify the accuracy of the theoretical analysis.