Finite difference methods for stochastic Helmholtz equation driven by white noise

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2024-09-20 DOI:10.1016/j.cam.2024.116286

Yanzhen Cui, Shibing Tang , Chao Zhang

引用次数: 0

Abstract

In this paper, we propose two numerical methods for the stochastic Helmholtz equation driven by white noise. We obtain the approximate stochastic problem by approximating the white noise with piecewise constant process, provide some regularity of its solution and the truncation error between the approximate stochastic problem and the original problem. The limitation on the wave number

k

of the finite difference method (FDM) is analyzed and a stochastic finite difference (SFD) scheme is presented. The error analysis shows that the stochastic finite difference method is efficient with a certain convergence rate. Numerical experiments are provided to examine our theoretical results.

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白噪声驱动的随机亥姆霍兹方程的有限差分法

本文针对白噪声驱动的随机亥姆霍兹方程提出了两种数值方法。我们通过用片断常数过程逼近白噪声得到近似随机问题，给出了其解的一些规律性以及近似随机问题与原问题之间的截断误差。分析了有限差分法（FDM）对波数 k 的限制，并提出了一种随机有限差分法（SFD）方案。误差分析表明，随机有限差分法具有一定的收敛效率。我们还提供了数值实验来检验我们的理论结果。

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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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.