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...

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Veröffentlicht in:Applied numerical mathematics Jg. 146; S. 182 - 198
Hauptverfasser: Saffarzadeh, M., Heydari, M., Loghmani, G.B.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.12.2019
Schlagworte:
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
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Zusammenfassung: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