{"title":"求解n维Wiener过程的非线性分数阶随机积分微分方程的一种数值方法","authors":"Elnaz Aryani, A. Babaei, Ali Valinejad","doi":"10.22034/CMDE.2020.41130.1784","DOIUrl":null,"url":null,"abstract":"This paper deals with the numerical solution of nonlinear fractional stochastic integro-differential equations with the n-dimensional Wiener process. A new computational method is employed to approximate the solution of the considered problem. This technique is based on the modified hat functions, the Caputo derivative and a suitable numerical integration rule. Error estimate of the method is investigated in detail. At the end, illustrative examples are included to demonstrate the validity and effectiveness of the presented approach.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2021-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"A numerical technique for solving nonlinear fractional stochastic integro-differential equations with n-dimensional Wiener process\",\"authors\":\"Elnaz Aryani, A. Babaei, Ali Valinejad\",\"doi\":\"10.22034/CMDE.2020.41130.1784\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper deals with the numerical solution of nonlinear fractional stochastic integro-differential equations with the n-dimensional Wiener process. A new computational method is employed to approximate the solution of the considered problem. This technique is based on the modified hat functions, the Caputo derivative and a suitable numerical integration rule. Error estimate of the method is investigated in detail. At the end, illustrative examples are included to demonstrate the validity and effectiveness of the presented approach.\",\"PeriodicalId\":44352,\"journal\":{\"name\":\"Computational Methods for Differential Equations\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2021-01-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational Methods for Differential Equations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22034/CMDE.2020.41130.1784\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Methods for Differential Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22034/CMDE.2020.41130.1784","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
A numerical technique for solving nonlinear fractional stochastic integro-differential equations with n-dimensional Wiener process
This paper deals with the numerical solution of nonlinear fractional stochastic integro-differential equations with the n-dimensional Wiener process. A new computational method is employed to approximate the solution of the considered problem. This technique is based on the modified hat functions, the Caputo derivative and a suitable numerical integration rule. Error estimate of the method is investigated in detail. At the end, illustrative examples are included to demonstrate the validity and effectiveness of the presented approach.