{"title":"用拟合算子格式数值处理抛物型奇摄动微分差分方程","authors":"D. Tefera, A. Tiruneh, G. A. Derese","doi":"10.1155/2021/1661661","DOIUrl":null,"url":null,"abstract":"This paper proposes a new fitted operator strategy for solving singularly perturbed parabolic partial differential equation with delay on the spatial variable. We decomposed the problem into three piecewise equations. The delay term in the equation is expanded by Taylor series, the time variable is discretized by implicit Euler method, and the space variable is discretized by central difference methods. After developing the fitting operator method, we accelerate the order of convergence of the time direction using Richardson extrapolation scheme and obtained uniform order of convergence. Finally, three examples are given to illustrate the effectiveness of the method. The result shows the proposed method is more accurate than some of the methods that exist in the literature.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":"2021 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Numerical Treatment on Parabolic Singularly Perturbed Differential Difference Equation via Fitted Operator Scheme\",\"authors\":\"D. Tefera, A. Tiruneh, G. A. Derese\",\"doi\":\"10.1155/2021/1661661\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper proposes a new fitted operator strategy for solving singularly perturbed parabolic partial differential equation with delay on the spatial variable. We decomposed the problem into three piecewise equations. The delay term in the equation is expanded by Taylor series, the time variable is discretized by implicit Euler method, and the space variable is discretized by central difference methods. After developing the fitting operator method, we accelerate the order of convergence of the time direction using Richardson extrapolation scheme and obtained uniform order of convergence. Finally, three examples are given to illustrate the effectiveness of the method. The result shows the proposed method is more accurate than some of the methods that exist in the literature.\",\"PeriodicalId\":7061,\"journal\":{\"name\":\"Abstract and Applied Analysis\",\"volume\":\"2021 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-10-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Abstract and Applied Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/2021/1661661\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Abstract and Applied Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2021/1661661","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
Numerical Treatment on Parabolic Singularly Perturbed Differential Difference Equation via Fitted Operator Scheme
This paper proposes a new fitted operator strategy for solving singularly perturbed parabolic partial differential equation with delay on the spatial variable. We decomposed the problem into three piecewise equations. The delay term in the equation is expanded by Taylor series, the time variable is discretized by implicit Euler method, and the space variable is discretized by central difference methods. After developing the fitting operator method, we accelerate the order of convergence of the time direction using Richardson extrapolation scheme and obtained uniform order of convergence. Finally, three examples are given to illustrate the effectiveness of the method. The result shows the proposed method is more accurate than some of the methods that exist in the literature.
期刊介绍:
Abstract and Applied Analysis is a mathematical journal devoted exclusively to the publication of high-quality research papers in the fields of abstract and applied analysis. Emphasis is placed on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, optimization theory, and control theory. Abstract and Applied Analysis supports the publication of original material involving the complete solution of significant problems in the above disciplines. Abstract and Applied Analysis also encourages the publication of timely and thorough survey articles on current trends in the theory and applications of analysis.