On partially inexact HSS iteration methods for the complex symmetric linear systems in space fractional CNLS equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:317

Article

Ran, Yu-Hong¹  Wang, Jun-Gang²  Wang, Dong-Ling¹ 

[1] Northwest Univ Xian, Sch Math, Ctr Nonlinear Studies, Xian 710127, Shaanxi, Peoples R China

[2] Northwestern Polytech Univ, Dept Appl Math, Xian 710072, Shaanxi, Peoples R China

关键词: The space fractional Schrodinger equations;    Hermitian and skew-Hermitian splitting;    Inexact iterations;    Conjugate gradient method;    Convergence analysis;   

DOI  :  10.1016/j.cam.2016.11.030

来源: Elsevier

【 摘 要 】

The space fractional coupled nonlinear Schrodinger (CNLS) equations are discretized by an implicit conservative difference scheme with the fractional centered difference formula, which is unconditionally stable. The coefficient matrix of the discretized linear system is equal to the sum of a complex scaled identity matrix and a symmetric positive definite diagonal-plus-Toeplitz matrix. The Hermitian and skew-Hermitian splitting (HSS) method and the partially inexact HSS (PIHSS) method are employed to solve the discretized linear system. In the inner iteration processes of the HSS method, we only need to solve the linear sub-systems associated with the Hermitian part inexactly by the conjugate gradient (CG) method, resulting in PIHSS iteration method. Theoretical analyses show that both HSS and PIHSS methods are unconditionally convergent. Numerical examples are given to demonstrate the effectiveness of the HSS iteration and the PIHSS iteration. (C) 2016 Elsevier B.V. All rights reserved.

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