Convergence of an Operator Splitting Scheme for Fractional Conservation Laws with Lévy Noise

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics Pub Date : 2024-04-02 DOI:10.1515/cmam-2023-0174

Soumya Ranjan Behera, Ananta K. Majee

引用次数: 0

Abstract

In this paper, we are concerned with an operator-splitting scheme for linear fractional and fractional degenerate stochastic conservation laws driven by multiplicative Lévy noise. More specifically, using a variant of the classical Kružkov doubling of variables approach, we show that the approximate solutions generated by the splitting scheme converge to the unique stochastic entropy solution of the underlying problems. Finally, the convergence analysis is illustrated by several numerical examples.

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具有莱维噪声的分数守恒定律的算子分裂方案的收敛性

在本文中，我们关注由乘法莱维噪声驱动的线性分数和分数退化随机守恒定律的算子分裂方案。更具体地说，利用经典的克鲁兹科夫变量倍增方法的变体，我们证明了分割方案生成的近似解收敛于基础问题的唯一随机熵解。最后，我们通过几个数值示例来说明收敛性分析。

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

Computational Methods in Applied Mathematics MATHEMATICS, APPLIED-

CiteScore

2.40

自引率

7.70%

发文量

期刊介绍： The highly selective international mathematical journal Computational Methods in Applied Mathematics　(CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics. The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.