梅立泉
- 教授
- Supervisor of Doctorate Candidates
- Supervisor of Master's Candidates
- E-Mail:
- Date of Employment:1997-07-01
- Education Level:With Certificate of Graduation for Doctorate Study
- Professional Title:教授
- Status:Employed
- Alma Mater:西安交通大学
- College:School Of Mathematics And Statistics
- Discipline:Mathematics
- Papers
Split-step spectral Galerkin method for the two-dimensional nonlinear space-fractional Schroedinger equation
Release Time:2025-04-30 Hits:
- Date:2025-04-30
- Title of Paper:Split-step spectral Galerkin method for the two-dimensional nonlinear space-fractional Schroedinger equation
- Journal:Applied Numerical Mathematics
- Summary:In this paper, we propose a highly accurate and conservative split-step spectral Galerkin (SSSG) scheme,
which combines the standard second-order Strang split-step method for handling the nonlinear and the
potential terms with the Legendre spectral Galerkin method for approximating the Riesz space-fractional
derivaties, for the two-dimensional nonlinear space-fractional Schr¨odinger equation. The mass conservation
property of the numerical solution is proved and the optimal error estimate with respect to spatial discretization
is established by introducing an orthogonal projection operator. In addition, a matrix diagonalization
technique is introduced to resolve the multi-dimensional difficulty and reduce the computational complexity
in the implementation. Numerical experiments are presented to illustrate the accuracy and robustness of
the SSSG method. - Co-author:Ying Wang, Liquan Mei, Qi Li, Linlin Bu
- Volume:136
- Page Number:257-278
- Translation or Not:No
- Date of Publication:2019-02-01