{"title":"带积分边界条件的二阶奇异扰动对流扩散方程的样条近似方法","authors":"A. Puvaneswari, T. Valanarasu","doi":"10.1007/s13226-024-00692-3","DOIUrl":null,"url":null,"abstract":"<p>In this work, we considered a Singular Perturbation Problem (SPP) with an integral boundary condition. Two numerical methods, namely Variable Mesh Spline Approximation Method (VMSAM) and Cubic B-Spline Collocation Method (CBSCM) are discussed to obtain second order convergence in the supremum norm. Numerical examples are presented to validate the obtained results.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"18 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Spline approximation methods for second order singularly perturbed convection-diffusion equation with integral boundary condition\",\"authors\":\"A. Puvaneswari, T. Valanarasu\",\"doi\":\"10.1007/s13226-024-00692-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this work, we considered a Singular Perturbation Problem (SPP) with an integral boundary condition. Two numerical methods, namely Variable Mesh Spline Approximation Method (VMSAM) and Cubic B-Spline Collocation Method (CBSCM) are discussed to obtain second order convergence in the supremum norm. Numerical examples are presented to validate the obtained results.</p>\",\"PeriodicalId\":501427,\"journal\":{\"name\":\"Indian Journal of Pure and Applied Mathematics\",\"volume\":\"18 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indian Journal of Pure and Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s13226-024-00692-3\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indian Journal of Pure and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s13226-024-00692-3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
在这项研究中，我们考虑了具有积分边界条件的奇异扰动问题（SPP）。我们讨论了两种数值方法，即可变网格样条逼近法（VMSAM）和立方 B 样条拼合法（CBSCM），以获得至上规范的二阶收敛。还给出了数值示例来验证所获得的结果。
Spline approximation methods for second order singularly perturbed convection-diffusion equation with integral boundary condition
In this work, we considered a Singular Perturbation Problem (SPP) with an integral boundary condition. Two numerical methods, namely Variable Mesh Spline Approximation Method (VMSAM) and Cubic B-Spline Collocation Method (CBSCM) are discussed to obtain second order convergence in the supremum norm. Numerical examples are presented to validate the obtained results.
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