Title: Numerical approach for solving nonlinear stochastic Itô-Volterra integral equations using shifted Legendre polynomials

Authors: Rebiha Zeghdane

Addresses: Faculty of Mathematics and Informatics, Department of Mathematics, University of Bordj Bou-Arreridj, Bordj Bou-Arreridj, 34265, El Anaser, Algeria

Abstract: In this paper, we give a new method for solving stochastic nonlinear Volterra integral equations by using shifted Legendre operational matrix. It is discussed that how the stochastic differential equations (SDE) could numerically be solved as matrix problems. By using this new operational matrix of integration and the so-called collocation method, nonlinear Volterra integral equations is reduced to systems of algebraic equations with unknown Legendre coefficients. Finally, the high accuracy of approximated solutions are illustrated by several experiment.

Keywords: stochastic Volterra integral equation; Brownian motion; approximate solution; best approximation; Legendre polynomials; collocation method.

DOI: 10.1504/IJDSDE.2021.113905

International Journal of Dynamical Systems and Differential Equations, 2021 Vol.11 No.1, pp.69 - 88

Received: 12 Sep 2018
Accepted: 07 May 2019
Published online: 01 Apr 2021 *

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