{"title":"A computational method for singularly perturbed reaction–diffusion type system of integro-differential equations with discontinuous source term","authors":"Ajay Singh Rathore, Vembu Shanthi","doi":"10.1007/s10092-024-00609-w","DOIUrl":null,"url":null,"abstract":"<p>This paper provides a qualitative and quantitative study of a second-order Singularly Perturbed Reaction–Diffusion type System of Integro-differential equations with discontinuous source term. To obtain the numerical solution of the problem, an exponentially-fitted method that can be applied to a Shishkin mesh. This method shows that uniform convergence with respect to the perturbation parameter and necessary examples are given.</p>","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Calcolo","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10092-024-00609-w","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper provides a qualitative and quantitative study of a second-order Singularly Perturbed Reaction–Diffusion type System of Integro-differential equations with discontinuous source term. To obtain the numerical solution of the problem, an exponentially-fitted method that can be applied to a Shishkin mesh. This method shows that uniform convergence with respect to the perturbation parameter and necessary examples are given.
期刊介绍：
Calcolo is a quarterly of the Italian National Research Council, under the direction of the Institute for Informatics and Telematics in Pisa. Calcolo publishes original contributions in English on Numerical Analysis and its Applications, and on the Theory of Computation.
The main focus of the journal is on Numerical Linear Algebra, Approximation Theory and its Applications, Numerical Solution of Differential and Integral Equations, Computational Complexity, Algorithmics, Mathematical Aspects of Computer Science, Optimization Theory.
Expository papers will also appear from time to time as an introduction to emerging topics in one of the above mentioned fields. There will be a "Report" section, with abstracts of PhD Theses, news and reports from conferences and book reviews. All submissions will be carefully refereed.
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