论文期刊

Split-step spectral Galerkin method for the two-dimensional nonlinear space-fractional Schroedinger equation




作者: Ying Wang, Liquan Mei, Qi Li, Linlin Bu
发表/完成日期: 2019-02-01
期刊名称: Applied Numerical Mathematics
期卷: 136
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论文简介
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.