A highly accurate symplectic-preserving scheme for Gross-Pitaevskii equation

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-09-03 DOI:10.1016/j.apnum.2025.08.006

Lan Wang , Yiyang Luo , Meng Chen , Pengfei Zhu

引用次数: 0

Abstract

An efficient fourth-order numerical scheme is developed for the Gross-Pitaevskii equation. The spatial direction is approximated by a fourth-order compact scheme and the temporal direction is discretized by a fourth-order splitting & composition method. This scheme not only preserves the symplectic structure and the discrete mass conservation law exactly but also maintains the discrete energy conservation law in some special case. Some numerical experiments confirm our theoretical expectation.

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Gross-Pitaevskii方程的高精度保辛格式

提出了Gross-Pitaevskii方程的一种有效的四阶数值格式。空间方向用四阶紧化格式逼近，时间方向用四阶分裂复合方法离散。该方案不仅准确地保持了辛结构和离散质量守恒定律，而且在某些特殊情况下也保持了离散能量守恒定律。一些数值实验证实了我们的理论预期。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.