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. [ABSTRACT FROM AUTHOR]