Recent advances in the numerical solution of the Nonlinear Schrödinger Equation

被引：0
|
作者：
Barletti, Luigi [1 ]
Brugnano, Luigi [1 ]
Gurioli, Gianmarco [1 ]
Iavernaro, Felice [2 ]
机构：
[1] Univ Firenze, Dipartimento Matemat & Informat U Dini, Florence, Italy
[2] Univ Bari Aldo Moro, Dipartimento Matemat, Bari, Italy
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2024年 / 445卷
关键词：
Nonlinear Schrodinger Equation; NLSE; Energy-conserving methods; Hamiltonian Boundary Value Methods; HBVMs; Spectral accuracy; BOUNDARY-VALUE METHODS; ENERGY-PRESERVING METHODS; BLENDED IMPLICIT METHODS; KUTTA-NYSTROM METHODS; SCHRODINGER-EQUATION; SYMPLECTIC METHODS; CONSERVING METHODS; GAUSS COLLOCATION; STEP METHODS; IMPLEMENTATION;
D O I：
10.1016/j.cam.2024.115826
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this review we collect some recent achievements in the accurate and efficient solution of the Nonlinear Schrodinger Equation (NLSE), with the preservation of its Hamiltonian structure. This is achieved by using the energy -conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs) after a proper space semi-discretization. The main facts about HBVMs, along with their application for solving the given problem, are here recalled and explained in detail. In particular, their use as spectral methods in time, which allows efficiently solving the problems with spectral space-time accuracy.
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页数：20
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