{"title":"Construction of a regularized asymptotic solution of an integro-differential equation with a rapidly oscillating cosine","authors":"A. Bobodzhanov, B. Kalimbetov, N. Pardaeva","doi":"10.22436/jmcs.032.01.07","DOIUrl":null,"url":null,"abstract":"In this paper, we consider a singularly perturbed integro-differential equation with a rapidly oscillating right-hand side, which includes an integral operator with a slowly varying kernel. Earlier, singularly perturbed differential and integro-differential equations with rapidly oscillating coefficients were considered. The main goal of this work is to generalize the Lomov's regularization method and to identify the rapidly oscillating right-hand side to the asymptotics of the solution to the original problem.","PeriodicalId":45497,"journal":{"name":"Journal of Mathematics and Computer Science-JMCS","volume":" ","pages":""},"PeriodicalIF":2.0000,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematics and Computer Science-JMCS","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22436/jmcs.032.01.07","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we consider a singularly perturbed integro-differential equation with a rapidly oscillating right-hand side, which includes an integral operator with a slowly varying kernel. Earlier, singularly perturbed differential and integro-differential equations with rapidly oscillating coefficients were considered. The main goal of this work is to generalize the Lomov's regularization method and to identify the rapidly oscillating right-hand side to the asymptotics of the solution to the original problem.