求解随机伊托-伏特拉积分方程的快速准确数值算法

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED

Numerical Algorithms Pub Date : 2024-07-29 DOI:10.1007/s11075-024-01898-6

Rebiha Zeghdane

{"title":"求解随机伊托-伏特拉积分方程的快速准确数值算法","authors":"Rebiha Zeghdane","doi":"10.1007/s11075-024-01898-6","DOIUrl":null,"url":null,"abstract":"<p>The purpose of this paper is to present a simple numerical technique for approximating the solutions of stochastic Volterra integral equations. The proposed method depends on the Picard iteration and uses a suitable quadrature rule. Error estimates and associated theorems have been proved for this proposed technique. Some test examples have been studied to verify the applicability and accuracy of the proposed technique.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"80 1","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fast and accurate numerical algorithm for solving stochastic Itô-Volterra integral equations\",\"authors\":\"Rebiha Zeghdane\",\"doi\":\"10.1007/s11075-024-01898-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The purpose of this paper is to present a simple numerical technique for approximating the solutions of stochastic Volterra integral equations. The proposed method depends on the Picard iteration and uses a suitable quadrature rule. Error estimates and associated theorems have been proved for this proposed technique. Some test examples have been studied to verify the applicability and accuracy of the proposed technique.</p>\",\"PeriodicalId\":54709,\"journal\":{\"name\":\"Numerical Algorithms\",\"volume\":\"80 1\",\"pages\":\"\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-07-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Numerical Algorithms\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11075-024-01898-6\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Numerical Algorithms","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11075-024-01898-6","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

本文旨在介绍一种用于逼近随机 Volterra 积分方程解的简单数值技术。所提出的方法依赖于 Picard 迭代，并使用合适的正交规则。本文证明了所提技术的误差估计和相关定理。研究了一些测试实例，以验证所提技术的适用性和准确性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Fast and accurate numerical algorithm for solving stochastic Itô-Volterra integral equations

查看原文本刊更多论文

Fast and accurate numerical algorithm for solving stochastic Itô-Volterra integral equations

The purpose of this paper is to present a simple numerical technique for approximating the solutions of stochastic Volterra integral equations. The proposed method depends on the Picard iteration and uses a suitable quadrature rule. Error estimates and associated theorems have been proved for this proposed technique. Some test examples have been studied to verify the applicability and accuracy of the proposed technique.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Numerical Algorithms 数学-应用数学

CiteScore

4.00

自引率

9.50%

发文量

201

审稿时长

9 months

期刊介绍： The journal Numerical Algorithms is devoted to numerical algorithms. It publishes original and review papers on all the aspects of numerical algorithms: new algorithms, theoretical results, implementation, numerical stability, complexity, parallel computing, subroutines, and applications. Papers on computer algebra related to obtaining numerical results will also be considered. It is intended to publish only high quality papers containing material not published elsewhere.