用富集谱Galerkin方法对几个奇摄动问题和奇异积分方程的高精度数值逼近

IF 0.8 4区数学

数学研究 Pub Date : 2020-06-01 DOI:10.4208/jms.v53n2.20.02

Sheng Chen sci

{"title":"用富集谱Galerkin方法对几个奇摄动问题和奇异积分方程的高精度数值逼近","authors":"Sheng Chen sci","doi":"10.4208/jms.v53n2.20.02","DOIUrl":null,"url":null,"abstract":"Usual spectral methods are not effective for singularly perturbed problems and singular integral equations due to the boundary layer functions or weakly singular solutions. To overcome this difficulty, the enriched spectral-Galerkin methods (ESG) are applied to deal with a class of singularly perturbed problems and singular integral equations for which the form of leading singular solutions can be determined. In particular, for easily understanding the technique of ESG, the detail of the process are provided in solving singularly perturbed problems. Ample numerical examples verify the efficiency and accuracy of the enriched spectral Galerkin methods. AMS subject classifications: 65N35, 65R20, 41A30","PeriodicalId":43526,"journal":{"name":"数学研究","volume":" ","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"High-Accuracy Numerical Approximations to Several Singularly Perturbed Problems and Singular Integral Equations by Enriched Spectral Galerkin Methods\",\"authors\":\"Sheng Chen sci\",\"doi\":\"10.4208/jms.v53n2.20.02\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Usual spectral methods are not effective for singularly perturbed problems and singular integral equations due to the boundary layer functions or weakly singular solutions. To overcome this difficulty, the enriched spectral-Galerkin methods (ESG) are applied to deal with a class of singularly perturbed problems and singular integral equations for which the form of leading singular solutions can be determined. In particular, for easily understanding the technique of ESG, the detail of the process are provided in solving singularly perturbed problems. Ample numerical examples verify the efficiency and accuracy of the enriched spectral Galerkin methods. AMS subject classifications: 65N35, 65R20, 41A30\",\"PeriodicalId\":43526,\"journal\":{\"name\":\"数学研究\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2020-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"数学研究\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4208/jms.v53n2.20.02\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"数学研究","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4208/jms.v53n2.20.02","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 3

摘要

由于边界层函数或弱奇异解的存在，通常的谱方法对奇异摄动问题和奇异积分方程的求解并不有效。为了克服这一困难，应用富谱伽辽金方法(ESG)处理了一类奇异摄动问题和可确定其前导奇异解形式的奇异积分方程。特别地，为了便于理解ESG技术，提供了解决奇异摄动问题的过程细节。数值算例验证了富谱伽辽金方法的有效性和准确性。AMS学科分类:65N35、65R20、41A30

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

High-Accuracy Numerical Approximations to Several Singularly Perturbed Problems and Singular Integral Equations by Enriched Spectral Galerkin Methods

Usual spectral methods are not effective for singularly perturbed problems and singular integral equations due to the boundary layer functions or weakly singular solutions. To overcome this difficulty, the enriched spectral-Galerkin methods (ESG) are applied to deal with a class of singularly perturbed problems and singular integral equations for which the form of leading singular solutions can be determined. In particular, for easily understanding the technique of ESG, the detail of the process are provided in solving singularly perturbed problems. Ample numerical examples verify the efficiency and accuracy of the enriched spectral Galerkin methods. AMS subject classifications: 65N35, 65R20, 41A30

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

数学研究 MATHEMATICS-

自引率

0.00%

发文量

1109

期刊介绍： Journal of Mathematical Study (JMS) is a comprehensive mathematical journal published jointly by Global Science Press and Xiamen University. It publishes original research and survey papers, in English, of high scientific value in all major fields of mathematics, including pure mathematics, applied mathematics, operational research, and computational mathematics.