Numerical approximation of \(p\)-dimensional stochastic Volterra integral equation using Walsh function

Volume 31, Issue 4, pp 448--460 http://dx.doi.org/10.22436/jmcs.031.04.07

Publication Date: May 24, 2023 Submission Date: March 24, 2023 Revision Date: April 18, 2023 Accteptance Date: May 10, 2023

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Authors

P. P. Paikaray - Department of Mathematics, College of Basic Science and Humanities, OUAT, Bhubaneswar, Odisha, 751003, India. S. Beuria - Department of Mathematics, College of Basic Science and Humanities, OUAT, Bhubaneswar, Odisha, 751003, India. N. Ch. Parida - Department of Mathematics, College of Basic Science and Humanities, OUAT, Bhubaneswar, Odisha, 751003, India.

Abstract

In this paper, we propose a numerical approach for solving \(p\)-dimensional stochastic Volterra integral equations using the Walsh function approximation. The main goal is to transform integral equations into an algebraic system and solve this further to get an approximate solution to the integral equation. The convergence and error analysis of the proposed method are studied for integral equations having functions in the Lipschitz class. The computation of various examples for which analytical solutions are available shows that the proposed method is more accurate than the existing techniques for solving linear \(p\)-dimensional stochastic Volterra integral equations.

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ISRP Style

P. P. Paikaray, S. Beuria, N. Ch. Parida, Numerical approximation of \(p\)-dimensional stochastic Volterra integral equation using Walsh function, Journal of Mathematics and Computer Science, 31 (2023), no. 4, 448--460

AMA Style

Paikaray P. P., Beuria S., Parida N. Ch., Numerical approximation of \(p\)-dimensional stochastic Volterra integral equation using Walsh function. J Math Comput SCI-JM. (2023); 31(4):448--460

Chicago/Turabian Style

Paikaray, P. P., Beuria, S., Parida, N. Ch.. "Numerical approximation of \(p\)-dimensional stochastic Volterra integral equation using Walsh function." Journal of Mathematics and Computer Science, 31, no. 4 (2023): 448--460

Keywords

Stochastic volterra integral equation
Brownian motion
Itô integral
Walsh approximation
Lipschitz condition

MSC

60H05
60H35
65C30

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