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Numerical solution of nonlinear stochastic integral equation of the third type with the help of operational matrix using Bernstein polynomials
(حل عددی معادله انتگرال تصادفی غیر خطی نوع سوم به کمک ماتریس عملیاتی با استفاده از چند جمله ای های برنشتاین)

Title	Numerical solution of nonlinear stochastic integral equation of the third type with the help of operational matrix using Bernstein polynomials
Title Original	حل عددی معادله انتگرال تصادفی غیر خطی نوع سوم به کمک ماتریس عملیاتی با استفاده از چند جمله ای های برنشتاین
Author	Morteza Khodabin ; Cup butterfly
Author Original	مرتضی خدابین پروانه جامی
Publication Date:	1400-10
Subject	Stochastic integral operational matrix, third type stochastic integral equation, Bernstein polynomials
Type	Periodical
Language	Persian
Digital	Yes
Manuscript	No
Library:	University of Toronto
Library Asset ID	ISSN: 2251-8088, EISSN: 2645-6141, DOI: 10.22055/jamm.2022.37847.1942
Record ID	cdi_doaj_primary_oai_doaj_org_article_29d8358b3f9c4f7a8eb77b2e263e5db9
Library Location	fulldisplay.datasource.DOAJ
Date	1400-10
Notes	In this article, we deal with the numerical solution of stochastic integral equations of the third type using the operational matrices of Bernstein polynomials. For this purpose, we first obtain the operational matrix and the stochastic operational matrix of Bernstein polynomials. We approximate all the functions in the stochastic integral equation of the third type using the series of Bernstein polynomials and then we use the operational matrices of Bernstein polynomials. With this, the solution of the random integral equation of the third type becomes the solution of a system of algebraic equations, which can be solved by Newton's method. The convergence analysis of the method is proposed and we provide two numerical examples to check the accuracy and efficiency of the method.
Erişim bilgileri	Available Online

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University of Toronto

Numerical solution of nonlinear stochastic integral equation of the third type with the help of operational matrix using Bernstein polynomials

(حل عددی معادله انتگرال تصادفی غیر خطی نوع سوم به کمک ماتریس عملیاتی با استفاده از چند جمله ای های برنشتاین)

Author Morteza Khodabin ; Cup butterfly

Author Original مرتضی خدابین پروانه جامی

Publication Date 1400-10

Subject Stochastic integral operational matrix, third type stochastic integral equation, Bernstein polynomials

Type Periodical

Language Persian

Digital Yes

Manuscript No

Library University of Toronto

Library Asset ID ISSN: 2251-8088, EISSN: 2645-6141, DOI: 10.22055/jamm.2022.37847.1942

Record ID cdi_doaj_primary_oai_doaj_org_article_29d8358b3f9c4f7a8eb77b2e263e5db9

Library Location fulldisplay.datasource.DOAJ

Date 1400-10

Notes In this article, we deal with the numerical solution of stochastic integral equations of the third type using the operational matrices of Bernstein polynomials. For this purpose, we first obtain the operational matrix and the stochastic operational matrix of Bernstein polynomials. We approximate all the functions in the stochastic integral equation of the third type using the series of Bernstein polynomials and then we use the operational matrices of Bernstein polynomials. With this, the solution of the random integral equation of the third type becomes the solution of a system of algebraic equations, which can be solved by Newton's method. The convergence analysis of the method is proposed and we provide two numerical examples to check the accuracy and efficiency of the method.

Erişim bilgileri Available Online