{"title":"求解带积分边界条件的奇异扰动 Volterra-Fredholm 积分微分方程的拟合近似法","authors":"Baransel Gunes, Musa Cakir","doi":"10.1007/s11253-024-02312-z","DOIUrl":null,"url":null,"abstract":"<p>We consider a novel numerical approach for solving boundary-value problems for the second-order Volterra-Fredholm integrodifferential equation with layer behavior and an integral boundary condition. A finite-difference scheme is proposed on suitable Shishkin-type mesh to obtain an approximate solution of the presented problem. It is proved that the method is first-order convergent in the discrete maximum norm. Two numerical examples are included to show the efficiency of the method.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"40 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Fitted Approximate Method for Solving Singularly Perturbed Volterra–Fredholm Integrodifferential Equations with Integral Boundary Condition\",\"authors\":\"Baransel Gunes, Musa Cakir\",\"doi\":\"10.1007/s11253-024-02312-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We consider a novel numerical approach for solving boundary-value problems for the second-order Volterra-Fredholm integrodifferential equation with layer behavior and an integral boundary condition. A finite-difference scheme is proposed on suitable Shishkin-type mesh to obtain an approximate solution of the presented problem. It is proved that the method is first-order convergent in the discrete maximum norm. Two numerical examples are included to show the efficiency of the method.</p>\",\"PeriodicalId\":49406,\"journal\":{\"name\":\"Ukrainian Mathematical Journal\",\"volume\":\"40 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-07-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ukrainian Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11253-024-02312-z\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ukrainian Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11253-024-02312-z","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
A Fitted Approximate Method for Solving Singularly Perturbed Volterra–Fredholm Integrodifferential Equations with Integral Boundary Condition
We consider a novel numerical approach for solving boundary-value problems for the second-order Volterra-Fredholm integrodifferential equation with layer behavior and an integral boundary condition. A finite-difference scheme is proposed on suitable Shishkin-type mesh to obtain an approximate solution of the presented problem. It is proved that the method is first-order convergent in the discrete maximum norm. Two numerical examples are included to show the efficiency of the method.
期刊介绍：
Ukrainian Mathematical Journal publishes articles and brief communications on various areas of pure and applied mathematics and contains sections devoted to scientific information, bibliography, and reviews of current problems. It features contributions from researchers from the Ukrainian Mathematics Institute, the major scientific centers of the Ukraine and other countries.
Ukrainian Mathematical Journal is a translation of the peer-reviewed journal Ukrains’kyi Matematychnyi Zhurnal, a publication of the Institute of Mathematics of the National Academy of Sciences of Ukraine.
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