Preconditioned modified Hermitian and skew-Hermitian splitting iteration methods for fractional nonlinear Schrodinger equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:367

Article

Wang, Zeng-Qi¹  Yin, Jun-Feng²  Dou, Quan-Yu² 

[1] Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai 200240, Peoples R China

[2] Tongji Univ, Sch Math Sci, Shanghai 200092, Peoples R China

关键词: The space fractional Schrodinger equations;    Toeplitz matrix;    HSS iteration methods;    Convergence analysis;    Preconditioning;   

DOI  :  10.1016/j.cam.2019.112420

来源: Elsevier

【 摘 要 】

A variant of preconditioned modified Hermitian and skew-Hermitian splitting (PMHSS) iteration method is proposed for a class of Toeplitz-like complex linear equations arising from the space fractional coupled nonlinear Schrodinger equations. Theoretical analysis show that the new method is convergent unconditionally. Moreover, the choice of the theoretical optimal parameter is further studied in detail, which minimize the upper bound of the spectral radius and relate to the extreme eigenvalues of the Toeplitz matrix and the extreme absolute values of the diagonal matrix. In addition, the splitting can be used as a preconditioner for Krylov subspaces method. Numerical experiments show that the proposed method is efficient, and the optimal parameter is independent of the mesh size which is very useful in large sparse practical problem. (C) 2019 Published by Elsevier B.V.

【 授权许可】

Free