Work

A split-step finite element method for the space-fractional Schrödinger equation in two dimensions

Year: 2024

Type: article

Abstract: In this article, we propose a split-step finite element method (FEM) for the two-dimensional nonlinear Schrödinger equation (NLS) with Riesz fractional derivatives in space. The space-fractional NLS is first spatially discretized by finite element scheme and the semi-discrete variational scheme is obtained. We prove that it maintains the mass and energy conservation laws. Then, we establish a fully discrete split-step finite element scheme for the considered problem, which avoids the iteration at each time layer, thereby significantly reducing computational cost. The discrete mass conservation property and error estimate of this split-step finite element scheme is derived. Finally, illustrative tests and the numerical simulation of dynamic of wave solutions are included to confirm its effectiveness and capability.

Source: Scientific Reports

DOI: 10.1038/s41598-024-75547-2

Authors: Xiaogang Zhu, Haiyang Wan, Yaping Zhang

Institutions: Shaoyang University, South China University of Technology

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,590

Funders: Natural Science Foundation of Hunan Province, Scientific Research Foundation of Hunan Provincial Education Department