The inverse problem and the second order [formula omitted] scheme with finite element method used for 2D nonlinear space fractional Schrödinger equation

Abstract

In this paper, we do research on the numerical analysis and the inverse problem for the two-dimensional nonlinear space fractional Schrödinger equation. The second order θ scheme combined with the unstructured mesh finite element method, which can cover the second order Crank–Nicolson method and the second order backward difference method in time, and can deal with the two-dimensional irregular region boundaries better in space, is used to obtain the numerical solution of the considered equation. On this basis, we introduce the Bayesian method to inverse the unknown parameters for the two-dimensional fractional Schrödinger equation. To testify the validity and efficiency of the proposed methods, a numerical example is conducted.