{"title":"带第三类延迟的弱奇异 Volterra 积分微分方程的分数谱方法","authors":"Borui Zhao","doi":"arxiv-2409.10861","DOIUrl":null,"url":null,"abstract":"In this paper, we present a fractional spectral collocation method for\nsolving a class of weakly singular Volterra integro-differential equations\n(VDIEs) with proportional delays and cordial operators. Assuming the underlying\nsolutions are in a specific function space, we derive error estimates in the\n$L^2_{\\omega^{\\alpha,\\beta,\\lambda}}$ and $L^{\\infty}$-norms. A rigorous proof\nreveals that the numerical errors decay exponentially with the appropriate\nselections of parameters $\\lambda$. Subsequently, numerical experiments are\nconducted to validate the effectiveness of the method.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"49 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Fractional spectral method for weakly singular Volterra integro-differential equations with delays of the third-kind\",\"authors\":\"Borui Zhao\",\"doi\":\"arxiv-2409.10861\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we present a fractional spectral collocation method for\\nsolving a class of weakly singular Volterra integro-differential equations\\n(VDIEs) with proportional delays and cordial operators. Assuming the underlying\\nsolutions are in a specific function space, we derive error estimates in the\\n$L^2_{\\\\omega^{\\\\alpha,\\\\beta,\\\\lambda}}$ and $L^{\\\\infty}$-norms. A rigorous proof\\nreveals that the numerical errors decay exponentially with the appropriate\\nselections of parameters $\\\\lambda$. Subsequently, numerical experiments are\\nconducted to validate the effectiveness of the method.\",\"PeriodicalId\":501162,\"journal\":{\"name\":\"arXiv - MATH - Numerical Analysis\",\"volume\":\"49 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Numerical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.10861\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10861","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Fractional spectral method for weakly singular Volterra integro-differential equations with delays of the third-kind
In this paper, we present a fractional spectral collocation method for
solving a class of weakly singular Volterra integro-differential equations
(VDIEs) with proportional delays and cordial operators. Assuming the underlying
solutions are in a specific function space, we derive error estimates in the
$L^2_{\omega^{\alpha,\beta,\lambda}}$ and $L^{\infty}$-norms. A rigorous proof
reveals that the numerical errors decay exponentially with the appropriate
selections of parameters $\lambda$. Subsequently, numerical experiments are
conducted to validate the effectiveness of the method.