{"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}
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Abstract
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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