求解单元球中某些偏微分方程的一种新的数值方法及其与有限元和精确解的比较

IF 1.4 Q2 MATHEMATICS, APPLIED

International Journal of Differential Equations Pub Date : 2021-04-09 DOI:10.1155/2021/6696165

R. Malek, C. Ziti

{"title":"求解单元球中某些偏微分方程的一种新的数值方法及其与有限元和精确解的比较","authors":"R. Malek, C. Ziti","doi":"10.1155/2021/6696165","DOIUrl":null,"url":null,"abstract":"In this paper, we give a new strategy to extend a numerical approximation method for two-dimensional reaction-diffusion problems. We present numerical results for this type of equations with a known analytical solution to qualify errors for the new method. We compare the results obtained using this approach to the standard finite element approach. +e proposed method is adequate even with the singular right-hand side of type Dirac.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":"2021 1","pages":"1-15"},"PeriodicalIF":1.4000,"publicationDate":"2021-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A New Numerical Method to Solve Some \\n \\n \\n PDE\\n \\n \\n s\\n \\n \\n in the Unit Ball and Comparison with the Finite Element and the Exact Solution\",\"authors\":\"R. Malek, C. Ziti\",\"doi\":\"10.1155/2021/6696165\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we give a new strategy to extend a numerical approximation method for two-dimensional reaction-diffusion problems. We present numerical results for this type of equations with a known analytical solution to qualify errors for the new method. We compare the results obtained using this approach to the standard finite element approach. +e proposed method is adequate even with the singular right-hand side of type Dirac.\",\"PeriodicalId\":55967,\"journal\":{\"name\":\"International Journal of Differential Equations\",\"volume\":\"2021 1\",\"pages\":\"1-15\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2021-04-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Differential Equations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/2021/6696165\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Differential Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2021/6696165","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 1

摘要

本文给出了一种新的策略来扩展二维反应扩散问题的数值逼近方法。我们给出了具有已知解析解的这类方程的数值结果，以限定新方法的误差。我们比较了用这种方法得到的结果与标准有限元方法。本文提出的方法即使对于狄拉克型的奇异右手边也是足够的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A New Numerical Method to Solve Some PDE s in the Unit Ball and Comparison with the Finite Element and the Exact Solution

In this paper, we give a new strategy to extend a numerical approximation method for two-dimensional reaction-diffusion problems. We present numerical results for this type of equations with a known analytical solution to qualify errors for the new method. We compare the results obtained using this approach to the standard finite element approach. +e proposed method is adequate even with the singular right-hand side of type Dirac.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

International Journal of Differential Equations MATHEMATICS, APPLIED-

CiteScore

3.10

自引率

0.00%

发文量

审稿时长

20 weeks