High order WSGL difference operators combined with Sinc-Galerkin method for time fractional Schrödinger equation

Abstract

ABSTRACT In this paper, high order time discretization schemes for time fractional Schrödinger equations in one and two dimensions are proposed. Our schemes are based on high order weighted and shifted Grünwald-Letnikov (WSGL) difference operators for the time fractional derivatives, Sinc-Galerkin methods are used for the space variables. The stability of time semi-discrete schemes is analysed with the help of -transform. For the fully discretization schemes, the standard Sinc-Galerkin method and symmetric Sinc-Galerkin method are established by selecting proper weight functions. Finally, we apply our numerical schemes to solve one-dimensional and two-dimensional time fractional Schrödinger equations, verify the validity of present numerical schemes.