Comparison of split-step and Hamiltonian integration methods for simulation of the nonlinear Schrodinger type equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:427

Article

Semenova, Anastassiya¹  Dyachenko, Sergey A.^3,4  Korotkevich, Alexander O.^1,2  Lushnikov, Pavel M.^1,2,5 

[1] Univ New Mexico, Dept Math & Stat, MSC01 1115,1 Univ New Mexico, Albuquerque, NM 87131 USA

[2] LD Landau Inst Theoret Phys, 2 Kosygin Str, Moscow 119334, Russia

[3] Univ Washington, Dept Appl Math, Lewis Hall 201,Box 353925, Seattle, WA 98195 USA

[4] SUNY Buffalo, Dept Math, 244 Math Bldg, Buffalo, NY 14260 USA

[5] NRU Higher Sch Econ, Myasnitskaya 20, Moscow 101000, Russia

关键词: Nonlinear Schrodinger equation;    Numerical methods;    Pseudospectral methods;    Computational physics;   

DOI  :  10.1016/j.jcp.2020.110061

来源: Elsevier

【 摘 要 】

We provide a systematic comparison of two numerical methods to solve the widely used nonlinear Schrodinger equation (NLSE). The first one is the standard second order split-step (SS2) method based on operator splitting approach. The second one is the Hamiltonian integration method (HIM), originally proposed in the paper by Dyachenko et al. (1992) [16]. Extension of the HIM to a widely used generalization of NLSE is developed. HIM allows the exact conservation of the Hamiltonian and wave action at the cost of requiring iterative solution for the implicit scheme. The numerical error for HIM is smaller than the SS2 solution for the same time step for almost all simulations we consider. Conversely, one can take orders of magnitude larger time steps in HIM, compared with SS2, still ensuring numerical stability. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free