Numerical Analysis of a Second-Order Algorithm for the Time-Dependent Natural Convection Problem

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics Pub Date : 2024-06-11 DOI:10.1515/cmam-2023-0225

Yiru Chen, Yun‐Bo Yang

引用次数: 0

Abstract

Abstract In this paper, a second-order algorithm based on the spectral deferred correction method is constructed for the time-dependent natural convection problem, which allows one to automatically increase the accuracy of a first-order backward-Euler time-stepping method through using spectral integration on Gaussian quadrature nodes and constructing the corrections. A complete theoretical analysis is presented to prove that this algorithm is unconditionally stable and possesses second-order accuracy in time. Numerical examples are given to confirm the theoretical analysis and the effectiveness of our algorithm.

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时变自然对流问题二阶算法的数值分析

摘要本文针对时变自然对流问题，构建了一种基于谱延迟修正法的二阶算法，通过在高斯正交节点上使用谱积分并构建修正，可以自动提高一阶后退-欧拉时步法的精度。通过完整的理论分析，证明该算法是无条件稳定的，并且在时间上具有二阶精度。还给出了数值示例来证实理论分析和算法的有效性。

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.