Energy-conserving methods for the nonlinear Schrodinger equation

被引：58

作者：

Barletti, L. ^{[1
]}

Brugnano, L. ^{[1
]}

Frasca Caccia, Gianluca ^{[2
]}

Iavernaro, F. ^{[3
]}

机构：

[1] Univ Firenze, Dipartimento Matemat & Informat U Dini, Florence, Italy

[2] Univ Kent, Sch Math Stat & Actuarial Sci, Canterbury, Kent, England

[3] Univ Bari, Dipartimento Matemat, Bari, Italy

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2018年 / 318卷

关键词：

Hamiltonian partial differential equations; Nonlinear Schrodinger equation; Energy-conserving methods; Line integral methods; Hamiltonian Boundary Value methods; HBVMs; NUMERICAL-SOLUTION; SYMPLECTIC METHODS; IMPLICIT METHODS; GAUSS COLLOCATION; STEP METHODS; INTEGRATORS; IMPLEMENTATION; FAMILY; HBVMS;

D O I：

10.1016/j.amc.2017.04.018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we further develop recent results in the numerical solution of Hamiltonian partial differential equations (PDEs) (Brugnano et al., 2015), by means of energy-conserving methods in the class of Line Integral Methods, in particular, the Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). We shall use HBVMs for solving the nonlinear Schrodinger equation (NLSE), of interest in many applications. We show that the use of energy-conserving methods, able to conserve a discrete counterpart of the Hamiltonian functional, confers more robustness on the numerical solution of such a problem. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：3 / 18

页数：16

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