用移位勒让德多项式求解非线性随机Itô-Volterra积分方程的数值方法

IF 0.2 Q4 MATHEMATICS, APPLIED

International Journal of Dynamical Systems and Differential Equations Pub Date : 2021-03-21 DOI:10.1504/IJDSDE.2021.10036610

R. Zeghdane

{"title":"用移位勒让德多项式求解非线性随机Itô-Volterra积分方程的数值方法","authors":"R. Zeghdane","doi":"10.1504/IJDSDE.2021.10036610","DOIUrl":null,"url":null,"abstract":"In this paper, we give a new method for solving stochastic nonlinear Volterra integral equations by using shifted Legendre operational matrix. It is discussed that how the stochastic differential equations (SDE) could numerically be solved as matrix problems. By using this new operational matrix of integration and the so-called collocation method, nonlinear Volterra integral equations is reduced to systems of algebraic equations with unknown Legendre coefficients. Finally, the high accuracy of approximated solutions are illustrated by several experiment.","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.2000,"publicationDate":"2021-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Numerical approach for solving nonlinear stochastic Itô-Volterra integral equations using shifted Legendre polynomials\",\"authors\":\"R. Zeghdane\",\"doi\":\"10.1504/IJDSDE.2021.10036610\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we give a new method for solving stochastic nonlinear Volterra integral equations by using shifted Legendre operational matrix. It is discussed that how the stochastic differential equations (SDE) could numerically be solved as matrix problems. By using this new operational matrix of integration and the so-called collocation method, nonlinear Volterra integral equations is reduced to systems of algebraic equations with unknown Legendre coefficients. Finally, the high accuracy of approximated solutions are illustrated by several experiment.\",\"PeriodicalId\":43101,\"journal\":{\"name\":\"International Journal of Dynamical Systems and Differential Equations\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.2000,\"publicationDate\":\"2021-03-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Dynamical Systems and Differential Equations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1504/IJDSDE.2021.10036610\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Dynamical Systems and Differential Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1504/IJDSDE.2021.10036610","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 1

摘要

本文给出了一种利用移位勒让德运算矩阵求解随机非线性Volterra积分方程的新方法。讨论了如何将随机微分方程(SDE)作为矩阵问题进行数值求解。利用这种新的积分运算矩阵和所谓的配置法，将非线性Volterra积分方程简化为具有未知勒让德系数的代数方程组。最后，通过实验验证了近似解的精度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Numerical approach for solving nonlinear stochastic Itô-Volterra integral equations using shifted Legendre polynomials

In this paper, we give a new method for solving stochastic nonlinear Volterra integral equations by using shifted Legendre operational matrix. It is discussed that how the stochastic differential equations (SDE) could numerically be solved as matrix problems. By using this new operational matrix of integration and the so-called collocation method, nonlinear Volterra integral equations is reduced to systems of algebraic equations with unknown Legendre coefficients. Finally, the high accuracy of approximated solutions are illustrated by several experiment.

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

International Journal of Dynamical Systems and Differential Equations MATHEMATICS, APPLIED-

CiteScore

0.80

自引率

0.00%

发文量

期刊介绍： IJDSDE is a quarterly international journal that publishes original research papers of high quality in all areas related to dynamical systems and differential equations and their applications in biology, economics, engineering, physics, and other related areas of science. Manuscripts concerned with the development and application innovative mathematical tools and methods from dynamical systems and differential equations, are encouraged.