Finite difference schemes for time-fractional Schrodinger equations via fractional linear multistep method

In this paper, a finite difference-based numerical approach is developed for time-fractional Schrodinger equations with one or multidimensional space variables, with the use of fractional linear multistep method for time discretization and finite difference method for spatial discretization. The proposed method leads to achieve second order of accuracy for time variable. Stability and convergence theorems for the constructed difference scheme is achieved via z-transform method. Time-fractional Schrodinger equation is considered in abstract form to allow generalization of the theoretical results on problems which have distinct spatial operators with or without variable coefficients. Numerical results are presented on one and multidimensional experimental problems to verify the theoretical results.

Automated summary

This paper presents a finite difference-based numerical approach for solving time-fractional Schrodinger equations with one or multidimensional space variables. The method achieves second order accuracy for time variable and ensures stability and convergence through the z-transform method. The approach can be extended to problems with different spatial operators or variable coefficients.