用于数学物理问题数值求解的新型经济无条件稳定分割法

IF 0.8 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI:10.1134/s1995080224602467

Ek. L. Kuznetsova, O. V. Egorova, A. S. Novikov

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引用次数: 0

摘要

摘要本文提出了一种经济的无条件稳定的变向外推法，用于求解含有混合导数的抛物线方程问题的数值解，并从近似性和稳定性方面进行了论证，在与其他数值方法的对比分析中，该方法在改变网格特性时显示出最高的精度和独特的稳定余量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

A New Economical Unconditional Stable Splitting Method for Numerical Solution of Problems of Mathematical Physics

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A New Economical Unconditional Stable Splitting Method for Numerical Solution of Problems of Mathematical Physics

Abstract

In this paper, an economical unconditionally stable method of variable directions with extrapolation of numerical solutions of problems for parabolic equations containing mixed derivatives is proposed and justified by approximation and stability, which, in comparative analysis with other numerical methods, showed the highest accuracy and a unique margin of stability when changing grid characteristics.

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来源期刊

Lobachevskii Journal of Mathematics MATHEMATICS-

CiteScore

1.50

自引率

42.90%

发文量

127

期刊介绍： Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.