Efficient time-splitting Hermite-Galerkin spectral method for the coupled nonlinear Schrödinger equations. (November 2020)

• Record Type: Journal Article
• Authors: Zhuang, Qingqu; Yang, Yi
• Is Part Of: Journal of algorithms & computational technology. Volume 14(2020)
• Publication Date: 2020-11
• Subjects: Coupled nonlinear Schrödinger equations -- Hermite-Galerkin spectral method -- discrete invariants -- splitting method; Computer algorithms -- Periodicals; Numerical calculations -- Periodicals; Computer algorithms; Numerical calculations; Periodicals; 518.1
• DOI: 10.1177/1748302620973532
• Languages: English
• ISSNs: 1748-3018

Abstract

The paper focuses on efficient time-splitting Hermite-Galerkin spectral approximation of the coupled nonlinear Schrödinger equations on the whole line. The original problem is decomposed into one nonlinear subproblem and one linear subproblem by time-splitting method. At each time step, the nonlinear subproblem is solved exactly. While the linear subproblem is efficiently solved by choosing suitable Hermite basis functions with matrix decomposition technique. Numerical experiments are carried out to demonstrate the effectiveness and efficiency of the proposed method.