## A Numerical Approximation of the Stochastic Ito-Volterra Integral Equation

Emmanuel Oladayo Oduselu–Hassan *

Department of Mathematics, Delta State University, Abraka, Nigeria.

Ignatius N. Njoseh

Department of Mathematics, Delta State University, Abraka, Nigeria.

Jonathan Tsetimi

Department of Mathematics, Delta State University, Abraka, Nigeria.

*Author to whom correspondence should be addressed.

### Abstract

A stochastic differential equation (SDE) is a differential equation in which one or more of the terms and the solution are stochastic processes. Numerous studies have employed orthogonal polynomials, however most of them focus on deterministic rather than stochastic systems. This is the reason why in this study, we looked into a numerical solution for the stochastic Ito-Volterra integral equation using the explicit finite difference scheme and Bernstein polynomials as trial functions. The equidistant collocation procedure was used to calculate the unknown constant parameters in between and reach the desired approximation. The method was evaluated and contrasted with the Block Pulse method for approximate answers based on the aforementioned method, which were obtained and compared with others in the literature.

Keywords: Process, Ito-Volterra integral equation, Stochastic Ito-Volterra integral equation, explicit finite difference scheme, Bernstein polynomials

**How to Cite**

*Asian Research Journal of Mathematics*,

*19*(11), 61–68. https://doi.org/10.9734/arjom/2023/v19i11753

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