Convergence analysis of an iterative numerical algorithm for solving nonlinear stochastic Itô-Volterra integral equations with m-dimensional Brownian motion

In this article, a numerical technique based on a combination of the Picard iteration method and hat basis functions to solve nonlinear stochastic Itô-Volterra integral equations with m-dimensional Brownian motion is proposed. The existence and uniqueness theorem for the solution of this class of It...

Full description

Saved in:

Bibliographic Details
Published in:	Applied numerical mathematics Vol. 146; pp. 182 - 198
Main Authors:	Saffarzadeh, M., Heydari, M., Loghmani, G.B.
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.12.2019
Subjects:	Hat basis functions Itô integral m-dimensional Brownian motion process Picard iteration method Stochastic Volterra integral equations Stochastic Volterra integral equations Itô integral Hat basis functions Picard iteration method m-dimensional Brownian motion process
ISSN:	0168-9274
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	In this article, a numerical technique based on a combination of the Picard iteration method and hat basis functions to solve nonlinear stochastic Itô-Volterra integral equations with m-dimensional Brownian motion is proposed. The existence and uniqueness theorem for the solution of this class of Itô-Volterra integral equations is proved. Also, convergence analysis of the suggested method is investigated in details. Finally, some numerical examples are provided to demonstrate the accuracy of the proposed method and guarantee the theoretical results.
ISSN:	0168-9274
DOI:	10.1016/j.apnum.2019.07.010