An efficient numerical method based on Lucas polynomials to solve multi-dimensional stochastic It?-Volterra integral equations

This article discusses the operational matrix method relying on Lucas polynomial to find the solution of multi-dimensional stochastic Ito-Volterra integral equation. For that purpose, the properties of Lucas polynomial and operational matrices have been investigated. Using Lucas polynomial based functions approximations and operational matrices along with collocation points, the multi-dimensional stochastic Ito-Volterra integral equation is converted into a linear or nonlinear system of algebraic equations. Convergence analysis of the presented method has been discussed. Numerical examples are examined to show their computational efficiency and accuracy. (c) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.