Structure-preserving Gauss methods for the nonlinear Schrodinger equation

被引：15

作者：

Akrivis, Georgios ^{[1
,2
]}

Li, Dongfang ^{[3
,4
]}

机构：

[1] Univ Ioannina, Dept Comp Sci & Engn, Ioannina 45110, Greece

[2] FORTH, Inst Appl & Computat Math, Iraklion 70013, Crete, Greece

[3] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

[4] Huazhong Univ Sci & Technol, Hubei Key Lab Engn Modeling & Sci Comp, Wuhan 430074, Peoples R China

来源：

CALCOLO | 2021年 / 58卷 / 02期

关键词：

Nonlinear Schrodinger equation; Gauss methods; Scalar auxiliary variable approach; Structure-preserving methods; L-2-conservative methods; Energy-conservative methods; Linearly implicit schemes; Continuous Galerkin method; FINITE-ELEMENT-METHOD; EXPONENTIAL INTEGRATORS; NUMERICAL SCHEMES; CONVERGENCE; 2ND-ORDER; SYSTEMS;

D O I：

10.1007/s10092-021-00405-w

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We use the scalar auxiliary variable (SAV) reformulation of the nonlinear Schrodinger (NLS) equation to construct structure-preserving SAV-Gauss methods for the NLS equation, namely L-2-conservative methods satisfying a discrete analogue of the energy (the Hamiltonian) conservation of the equation. This is in contrast to Gauss methods for the standard form of the NLS equation that are L-2-conservative but not energy-conservative. We also discuss efficient linearizations of the new methods and their conservation properties.

引用

页数：25

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