{"title":"基于移位Jacobi多项式求分数阶布朗运动驱动非线性随机微分方程数值解的新研究","authors":"P. K. Singh, S. Saha Ray","doi":"10.1515/cmam-2022-0187","DOIUrl":null,"url":null,"abstract":"Abstract The main objective of this article is to represent an efficient numerical approach based on shifted Jacobi polynomials to solve nonlinear stochastic differential equations driven by fractional Brownian motion. In this method, function approximation and operational matrices based on shifted Jacobi polynomials have been studied, which are further used with appropriate collocation points to reduce nonlinear stochastic differential equations driven by fractional Brownian motion into a system of algebraic equations. Newton’s method has been used to solve this nonlinear system of equations, and the desired approximate solution is achieved. Moreover, the error and convergence analysis of the presented method are also established in detail. Additionally, the applicability of the proposed method is demonstrated by solving some numerical examples.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"23 1","pages":"715 - 728"},"PeriodicalIF":1.0000,"publicationDate":"2023-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"A Novel Study Based on Shifted Jacobi Polynomials to Find the Numerical Solutions of Nonlinear Stochastic Differential Equations Driven by Fractional Brownian Motion\",\"authors\":\"P. K. Singh, S. Saha Ray\",\"doi\":\"10.1515/cmam-2022-0187\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract The main objective of this article is to represent an efficient numerical approach based on shifted Jacobi polynomials to solve nonlinear stochastic differential equations driven by fractional Brownian motion. In this method, function approximation and operational matrices based on shifted Jacobi polynomials have been studied, which are further used with appropriate collocation points to reduce nonlinear stochastic differential equations driven by fractional Brownian motion into a system of algebraic equations. Newton’s method has been used to solve this nonlinear system of equations, and the desired approximate solution is achieved. Moreover, the error and convergence analysis of the presented method are also established in detail. Additionally, the applicability of the proposed method is demonstrated by solving some numerical examples.\",\"PeriodicalId\":48751,\"journal\":{\"name\":\"Computational Methods in Applied Mathematics\",\"volume\":\"23 1\",\"pages\":\"715 - 728\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-01-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational Methods in Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/cmam-2022-0187\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Methods in Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/cmam-2022-0187","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
A Novel Study Based on Shifted Jacobi Polynomials to Find the Numerical Solutions of Nonlinear Stochastic Differential Equations Driven by Fractional Brownian Motion
Abstract The main objective of this article is to represent an efficient numerical approach based on shifted Jacobi polynomials to solve nonlinear stochastic differential equations driven by fractional Brownian motion. In this method, function approximation and operational matrices based on shifted Jacobi polynomials have been studied, which are further used with appropriate collocation points to reduce nonlinear stochastic differential equations driven by fractional Brownian motion into a system of algebraic equations. Newton’s method has been used to solve this nonlinear system of equations, and the desired approximate solution is achieved. Moreover, the error and convergence analysis of the presented method are also established in detail. Additionally, the applicability of the proposed method is demonstrated by solving some numerical examples.
期刊介绍:
The highly selective international mathematical journal Computational Methods in Applied Mathematics (CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs.
CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics.
The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.