Mathematical analysis of a norm-conservative numerical scheme for the Ostrovsky equation

IF 0.7 4区数学 Q3 MATHEMATICS, APPLIED

Japan Journal of Industrial and Applied Mathematics Pub Date : 2024-09-02 DOI:10.1007/s13160-024-00669-z

Shuto Kawai, Shun Sato, Takayasu Matsuo

引用次数: 0

Abstract

The target of this study is a norm-conservative scheme for the Ostrovsky equation, as its mathematical analysis has not been addressed. First, the existence and uniqueness of its numerical solutions are demonstrated. Subsequently, a convergence estimate in the two-norm is established. This, in turn, implies a convergence in the first-order Sobolev space using a supplementary sup-norm boundedness argument. Finally, this conservative scheme can be implemented in a differential form, which is considerably better than the integral form in terms of computational cost-effectiveness.

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奥斯特洛夫斯基方程的规范保守数值方案的数学分析

本研究的目标是奥斯特洛夫斯基方程的规范保守方案，因为其数学分析尚未涉及。首先，证明了其数值解的存在性和唯一性。随后，建立了二规范的收敛估计。这反过来又意味着使用补充的超规范有界性论证在一阶 Sobolev 空间中的收敛性。最后，这种保守方案可以微分形式实现，在计算成本效益方面大大优于积分形式。

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

Japan Journal of Industrial and Applied Mathematics 数学-应用数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： Japan Journal of Industrial and Applied Mathematics (JJIAM) is intended to provide an international forum for the expression of new ideas, as well as a site for the presentation of original research in various fields of the mathematical sciences. Consequently the most welcome types of articles are those which provide new insights into and methods for mathematical structures of various phenomena in the natural, social and industrial sciences, those which link real-world phenomena and mathematics through modeling and analysis, and those which impact the development of the mathematical sciences. The scope of the journal covers applied mathematical analysis, computational techniques and industrial mathematics.