{"title":"具有弱奇异核的延迟 Volterra 积分方程配位解的收敛性分析","authors":"P. Peyrovan , A. Tari , H. Brunner","doi":"10.1016/j.amc.2024.129122","DOIUrl":null,"url":null,"abstract":"<div><div>Convergence analysis of the collocation solutions for second-kind Volterra integral equations (VIEs) with weakly singular kernels (WSKs) in continuous piecewise polynomial space (PPS) under certain conditions on the collocation parameters has been established previously. In this paper, we study the analogue convergence analysis for delay Volterra integral equations (DVIEs) with WSKs and vanishing delay. We also investigate the existence, uniqueness and regularity of solution. Finally, we present some illustrative numerical examples to confirm the theoretical results.</div></div>","PeriodicalId":3,"journal":{"name":"ACS Applied Electronic Materials","volume":null,"pages":null},"PeriodicalIF":4.3000,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Convergence analysis of collocation solutions for delay Volterra integral equations with weakly singular kernels\",\"authors\":\"P. Peyrovan , A. Tari , H. Brunner\",\"doi\":\"10.1016/j.amc.2024.129122\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Convergence analysis of the collocation solutions for second-kind Volterra integral equations (VIEs) with weakly singular kernels (WSKs) in continuous piecewise polynomial space (PPS) under certain conditions on the collocation parameters has been established previously. In this paper, we study the analogue convergence analysis for delay Volterra integral equations (DVIEs) with WSKs and vanishing delay. We also investigate the existence, uniqueness and regularity of solution. Finally, we present some illustrative numerical examples to confirm the theoretical results.</div></div>\",\"PeriodicalId\":3,\"journal\":{\"name\":\"ACS Applied Electronic Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.3000,\"publicationDate\":\"2024-10-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Electronic Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0096300324005836\",\"RegionNum\":3,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, ELECTRICAL & ELECTRONIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Electronic Materials","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0096300324005836","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
Convergence analysis of collocation solutions for delay Volterra integral equations with weakly singular kernels
Convergence analysis of the collocation solutions for second-kind Volterra integral equations (VIEs) with weakly singular kernels (WSKs) in continuous piecewise polynomial space (PPS) under certain conditions on the collocation parameters has been established previously. In this paper, we study the analogue convergence analysis for delay Volterra integral equations (DVIEs) with WSKs and vanishing delay. We also investigate the existence, uniqueness and regularity of solution. Finally, we present some illustrative numerical examples to confirm the theoretical results.
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