{"title":"Fitted Operator Average Finite Difference Method for Singularly Perturbed Delay Parabolic Reaction Diffusion Problems with Non-Local Boundary Conditions","authors":"Wakjira Tolassa Gobena, G. Duressa","doi":"10.5556/j.tkjm.54.2023.4175","DOIUrl":null,"url":null,"abstract":"This paper deals with numerical solution of singularly perturbed delay parabolic reaction diffusion problem having large delay on the spatial variable with non-local boundary condition. The solution of the problem exhibits parabolic boundary layer on both sides of the spatial domain and interior layer is also created. Introducing a fitting parameter into asymptotic solution and applying average finite difference approximation, a fitted operator finite difference method is developed for solving the problem under consideration. To treat the non-local boundary condition, Simpson's rule is applied. The stability and $\\varepsilon$ uniform convergence analysis has been carried out. To validate the applicability of the scheme, numerical examples are presented and solved for different values of the perturbation parameter $\\varepsilon$ and mesh sizes. The numerical results are tabulated in terms of maximum absolute errors and rate of convergence and it is observed that the present method is more accurate and shown to be second order Uniformly convergent in both direction, and it also improves the results of the methods existing in the literature.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2022-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tamkang Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5556/j.tkjm.54.2023.4175","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 5
Abstract
This paper deals with numerical solution of singularly perturbed delay parabolic reaction diffusion problem having large delay on the spatial variable with non-local boundary condition. The solution of the problem exhibits parabolic boundary layer on both sides of the spatial domain and interior layer is also created. Introducing a fitting parameter into asymptotic solution and applying average finite difference approximation, a fitted operator finite difference method is developed for solving the problem under consideration. To treat the non-local boundary condition, Simpson's rule is applied. The stability and $\varepsilon$ uniform convergence analysis has been carried out. To validate the applicability of the scheme, numerical examples are presented and solved for different values of the perturbation parameter $\varepsilon$ and mesh sizes. The numerical results are tabulated in terms of maximum absolute errors and rate of convergence and it is observed that the present method is more accurate and shown to be second order Uniformly convergent in both direction, and it also improves the results of the methods existing in the literature.
期刊介绍:
To promote research interactions between local and overseas researchers, the Department has been publishing an international mathematics journal, the Tamkang Journal of Mathematics. The journal started as a biannual journal in 1970 and is devoted to high-quality original research papers in pure and applied mathematics. In 1985 it has become a quarterly journal. The four issues are out for distribution at the end of March, June, September and December. The articles published in Tamkang Journal of Mathematics cover diverse mathematical disciplines. Submission of papers comes from all over the world. All articles are subjected to peer review from an international pool of referees.