{"title":"A modification of Durán-type mesh for singularly perturbed problems","authors":"G. Radojev , M. Brdar , Lj. Teofanov","doi":"10.1016/j.amc.2025.129339","DOIUrl":null,"url":null,"abstract":"<div><div>A new approach to the Durán-type mesh is presented in order to improve the standard definition of this layer-adjusted mesh and eliminate some of its drawbacks. The construction of this graded mesh is provided for an elliptic convection-diffusion problem, a convection-diffusion-reaction problem, a third-order problem, and a convection-diffusion problem with a large shift. Our modification outperforms the standard Durán-type mesh both theoretically and numerically. Furthermore, the modified mesh is unique and allows for a fair comparison of numerical results obtained with other meshes of the Shishkin and Bakhvalov-types.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"495 ","pages":"Article 129339"},"PeriodicalIF":3.5000,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Computation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0096300325000669","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
A new approach to the Durán-type mesh is presented in order to improve the standard definition of this layer-adjusted mesh and eliminate some of its drawbacks. The construction of this graded mesh is provided for an elliptic convection-diffusion problem, a convection-diffusion-reaction problem, a third-order problem, and a convection-diffusion problem with a large shift. Our modification outperforms the standard Durán-type mesh both theoretically and numerically. Furthermore, the modified mesh is unique and allows for a fair comparison of numerical results obtained with other meshes of the Shishkin and Bakhvalov-types.
期刊介绍：
Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results.
In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.
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