{"title":"Numerical Analysis of a Second-Order Algorithm for the Time-Dependent Natural Convection Problem","authors":"Yiru Chen, Yun‐Bo Yang","doi":"10.1515/cmam-2023-0225","DOIUrl":null,"url":null,"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.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Methods in Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/cmam-2023-0225","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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.
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.
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