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Compact splitting symplectic scheme for the fourth-order dispersive Schrödinger equation with Cubic-Quintic nonlinear term

Fujian Province University Key Laboratory, of Computational Science, School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, P. R. China

Key Laboratory of Applied Mathematics, (Putian University), Fujian Province University, Fujian Putian 351100, P. R. China

E-mail Address: hlyang@hqu.edu.cn

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Zhi-Feng Weng

Fujian Province University Key Laboratory, of Computational Science, School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, P. R. China

E-mail Address: zfwmath@163.com

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Chao-Ying Lin

Fujian Province University Key Laboratory, of Computational Science, School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, P. R. China

E-mail Address: 820576332@qq.com

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https://doi.org/10.1142/S1793962319500077Cited by:1 (Source: Crossref)

This article is part of the issue:

Special Section on SIMULTECH; Guest Editors: Mohammad S. Obaidat, Floriano De Rango and Tuncer Oren

Abstract

Combining symplectic algorithm, splitting technique and compact method, a compact splitting symplectic scheme is proposed to solve the fourth-order dispersive Schrödinger equation with cubic-quintic nonlinear term. The scheme has fourth-order accuracy in space and second-order accuracy in time. The discrete charge conservation law and stability of the scheme are analyzed. Numerical examples are given to confirm the theoretical results.

Keywords:

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