Superconvergence analysis of a linearized energy-conservative Galerkin method for the nonlinear Schriidinger equation with wave operator

被引：3

作者：

Yang, Huaijun ^{[1
]}

Wang, Lele ^{[1
]}

Liao, Xin ^{[1
]}

机构：

[1] Zhengzhou Univ Aeronaut, Sch Math, Zhengzhou 450046, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2023年 / 133卷

基金：

中国国家自然科学基金;

关键词：

Nonlinear Schriidinger equation with wave operator; Linearized energy-conservative scheme; Unconditionally superconvergence error estimates; FINITE-DIFFERENCE METHODS; MODELING LIGHT BULLETS; SCHRODINGER-EQUATION; ERROR ANALYSIS; UNCONDITIONAL CONVERGENCE; SINE-GORDON; FEMS; SCHEME; APPROXIMATION; STABILITY;

D O I：

10.1016/j.camwa.2023.01.024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, based on a modified leap-frog scheme used in temporal direction and bilinear rectangular element applied in spatial direction, the superconvergence of Galerkin approximation are investigated for the cubic nonlinear Schrodinger equation with wave operator. The key issue to our analysis is to obtain the boundedness of the numerical solution in H-1- norm, which is indeed different from the boundedness of the L-infinity- norm required in the previous literatures. The unconditionally superconvergence error estimates are obtained without any restrictions between time stepsize and spatial meshsize. Finally, some numerical results are provided to support the theoretical analysis.

引用

页码：142 / 154

页数：13

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