随机 KdV 方程的结构保持局部非连续伽勒金方法

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED Applied Numerical Mathematics Pub Date : 2024-06-06 DOI:10.1016/j.apnum.2024.06.001

Xuewei Liu , Zhanwen Yang , Qiang Ma , Xiaohua Ding

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引用次数: 0

摘要

本文针对具有多维乘法噪声的随机 Korteweg-de Vries（KdV）方程提出了一种局部非连续 Galerkin（LDG）方法。从均方意义上讲，我们证明了该数值方法是 L2 稳定的，并且保持了能量守恒和能量耗散。如果多项式的阶数为 n，均方意义上的最优误差估计值可达 n+1。最后，通过数值实验验证了结构保持性和收敛性。

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A structure-preserving local discontinuous Galerkin method for the stochastic KdV equation

This paper proposes a local discontinuous Galerkin (LDG) method for the stochastic Korteweg-de Vries (KdV) equation with multi-dimensional multiplicative noise. In the mean square sense, we show that the numerical method is $L^{2}$ stable and it preserves energy conservation and energy dissipation. If the degree of the polynomial is n, the optimal error estimate in the mean square sense can reach as $n + 1$ . Finally, structure-preserving and convergence are verified by numerical experiments.

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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.

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