A structure-preserving Fourier pseudo-spectral linearly implicit scheme for the space-fractional nonlinear Schrödinger equation

IF 1 Q3 Engineering

Journal of Computational Dynamics Pub Date : 2019-02-21 DOI:10.3934/jcd.2019018

Y. Miyatake, T. Nakagawa, T. Sogabe, Shaoliang Zhang

引用次数: 6

Abstract

We propose a Fourier pseudo-spectral scheme for the space-fractional nonlinear Schr\"odinger equation. The proposed scheme has the following features: it is linearly implicit, it preserves two invariants of the equation, its unique solvability is guaranteed without any restrictions on space and time step sizes. The scheme requires solving a complex symmetric linear system per time step. To solve the system efficiently, we also present a certain variable transformation and preconditioner.

查看原文本刊更多论文

空间分数阶非线性Schrödinger方程的保结构傅立叶伪谱线性隐式格式

提出了空间分数阶非线性Schr\ odinger方程的傅里叶伪谱格式。该方案具有以下特点:线性隐式，保持方程的两个不变量，保证其唯一可解性，不受时间和空间步长的限制。该方案要求每个时间步长求解一个复杂的对称线性系统。为了有效地求解该系统，我们还提出了一定的变量变换和预条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Computational Dynamics Engineering-Computational Mechanics

CiteScore

2.30

自引率

10.00%

发文量

期刊介绍： JCD is focused on the intersection of computation with deterministic and stochastic dynamics. The mission of the journal is to publish papers that explore new computational methods for analyzing dynamic problems or use novel dynamical methods to improve computation. The subject matter of JCD includes both fundamental mathematical contributions and applications to problems from science and engineering. A non-exhaustive list of topics includes * Computation of phase-space structures and bifurcations * Multi-time-scale methods * Structure-preserving integration * Nonlinear and stochastic model reduction * Set-valued numerical techniques * Network and distributed dynamics JCD includes both original research and survey papers that give a detailed and illuminating treatment of an important area of current interest. The editorial board of JCD consists of world-leading researchers from mathematics, engineering, and science, all of whom are experts in both computational methods and the theory of dynamical systems.