A stable numerical method for multidimensional time fractional Schrödinger equations

In this paper, the stability analysis is presented for a first order difference scheme applied to a nonhomogeneous time fractional Schrödinger differential equation. Based on the z-transform method, stability theorems are proved for the abstract case. The stability results are applied on initial-boundary value problems for multidimensional time fractional Schrödinger differential equations. Theoretical findings are validated by numerical experiments on one and two-dimensional time fractional Schrödinger differential equations.