受乘法时空噪声影响的阻尼非线性随机波方程的新型显式全离散动量保全方案

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2024-09-28 DOI:10.1016/j.aml.2024.109325

Feng Wang, Zhenyu Wang, Qiang Ma, Xiaohua Ding

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引用次数: 0

摘要

本文推导了受乘法时空噪声影响的阻尼非线性随机波方程（DNSWE）的全局动量和平均全局动量的演化规律。我们创新性地在空间上结合了二阶中心有限差分法和离散梯度法，在时间上集成了分裂法和 Störmer-Verlet 类型法。这样构建的新型空间半离散方案和全离散方案都能成功保留离散全局动量和离散平均全局动量的相应演化规律。对具有立方非线性的 DNSWE 的数值实验验证了理论结果。

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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A novel explicit fully-discrete momentum-preserving scheme of damped nonlinear stochastic wave equation influenced by multiplicative space-time noise

In this paper, the evolution laws of global momentum and averaged global momentum for the damped nonlinear stochastic wave equation (DNSWE) influenced by multiplicative space-time noise are derived. We innovatively combine the second-order central finite difference method and discrete gradient method in space, and integrate the splitting method and Störmer-Verlet type method in time. Both the novel spatial semi-discrete scheme and fully-discrete scheme constructed in this way can successfully preserve the corresponding evolution laws for discrete global momentum and discrete averaged global momentum. Numerical experiments on DNSWE with cubic nonlinearity validate the theoretical results.

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.