ADM-TF hybrid method for nonlinear Ito-Volterra integral equations

In this paper, a new combination method is being proposed for the numerical solution of nonlinear Ito-Volterra stochastic integral equations based on Adomian decomposition method (ADM), Triangular function (TF) approximation, quadrature methods and Ito stochastic integration formula. The presented method is developed in two steps. First, we apply ADM to the main equation then for calculating the components, we used TF-approximation together with quadrature and Ito stochastic integration formula. Some theorems related to error and convergence analysis of the suggested method are also stated. Finally, several examples confirm the applicability, efficiency and accuracy of the method, along with comparisons. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.