On the Comparison of Two Meshless Finite Difference Methods for Solving Shallow Water Equations

IF 0.7 4区数学 Q2 MATHEMATICS

Bulletin of The Iranian Mathematical Society Pub Date : 2024-01-04 DOI:10.1007/s41980-023-00839-8

Juan José Benito, Ángel García, Mihaela Negreanu, Francisco Ureña, Antonio Manuel Vargas

引用次数: 0

Abstract

In this article, we present a numerical analysis of the Korteweg-de Vries (KdV) and Regularized Long Wave (RLW) equations using a finite difference space-time method. The KdV and RLW equations are partial differential equations that describe the behavior of long shallow water waves. We show that the finite difference space-time method is an effective way to solve these equations numerically, and we compare the results with those obtained using explicit method and generalized finite difference (GFD) formulae. Our results indicate that the finite difference space-time method provides accurate and stable solutions for both the KdV and RLW equations.

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关于两种求解浅水方程的无网格有限差分法的比较

本文采用有限差分时空法对 Korteweg-de Vries（KdV）和 Regularized Long Wave（RLW）方程进行了数值分析。KdV 和 RLW 方程是描述浅水长波行为的偏微分方程。我们证明有限差分时空法是数值求解这些方程的有效方法，并将其结果与使用显式方法和广义有限差分（GFD）公式求解的结果进行了比较。我们的结果表明，有限差分时空法为 KdV 和 RLW 方程提供了精确而稳定的解。

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

Bulletin of The Iranian Mathematical Society Mathematics-General Mathematics

CiteScore

1.40

自引率

0.00%

发文量

期刊介绍： The Bulletin of the Iranian Mathematical Society (BIMS) publishes original research papers as well as survey articles on a variety of hot topics from distinguished mathematicians. Research papers presented comprise of innovative contributions while expository survey articles feature important results that appeal to a broad audience. Articles are expected to address active research topics and are required to cite existing (including recent) relevant literature appropriately. Papers are critically reviewed on the basis of quality in its exposition, brevity, potential applications, motivation, value and originality of the results. The BIMS takes a high standard policy against any type plagiarism. The editorial board is devoted to solicit expert referees for a fast and unbiased review process.