{"title":"大时滞奇摄动时滞微分方程的拟合参数指数样条法","authors":"E. Siva Prasad, R. Omkar, Kolloju Phaneendra","doi":"10.1155/2022/9291834","DOIUrl":null,"url":null,"abstract":"<div>\n <p>In this paper, we present a new computational method based on an exponential spline for solving a class of delay differential equations with a negative shift in the differentiated term. When the shift parameter is <i>O</i>(<i>ε</i>), the proposed method works well and also controls the oscillations in the solution’s layer region. To accomplish this, we included a parameter in the proposed numerical scheme that is based on a special type of mesh, and the parameter is evaluated using the theory of singular perturbation. Maximum absolute errors and convergences of numerical solutions are tabulated to demonstrate the efficiency of the proposed computational method and to support the convergence analysis of the presented scheme.</p>\n </div>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2022 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2022-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2022/9291834","citationCount":"0","resultStr":"{\"title\":\"Fitted Parameter Exponential Spline Method for Singularly Perturbed Delay Differential Equations with a Large Delay\",\"authors\":\"E. Siva Prasad, R. Omkar, Kolloju Phaneendra\",\"doi\":\"10.1155/2022/9291834\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>\\n <p>In this paper, we present a new computational method based on an exponential spline for solving a class of delay differential equations with a negative shift in the differentiated term. When the shift parameter is <i>O</i>(<i>ε</i>), the proposed method works well and also controls the oscillations in the solution’s layer region. To accomplish this, we included a parameter in the proposed numerical scheme that is based on a special type of mesh, and the parameter is evaluated using the theory of singular perturbation. Maximum absolute errors and convergences of numerical solutions are tabulated to demonstrate the efficiency of the proposed computational method and to support the convergence analysis of the presented scheme.</p>\\n </div>\",\"PeriodicalId\":100308,\"journal\":{\"name\":\"Computational and Mathematical Methods\",\"volume\":\"2022 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2022-08-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2022/9291834\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational and Mathematical Methods\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1155/2022/9291834\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational and Mathematical Methods","FirstCategoryId":"1085","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1155/2022/9291834","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Fitted Parameter Exponential Spline Method for Singularly Perturbed Delay Differential Equations with a Large Delay
In this paper, we present a new computational method based on an exponential spline for solving a class of delay differential equations with a negative shift in the differentiated term. When the shift parameter is O(ε), the proposed method works well and also controls the oscillations in the solution’s layer region. To accomplish this, we included a parameter in the proposed numerical scheme that is based on a special type of mesh, and the parameter is evaluated using the theory of singular perturbation. Maximum absolute errors and convergences of numerical solutions are tabulated to demonstrate the efficiency of the proposed computational method and to support the convergence analysis of the presented scheme.