Numerical approach for solving nonlinear stochastic Ito-Volterra integral equations using Fibonacci operational matrices

Abstract

This article proposes an efficient method based on the Fibonacci functions for solving nonlinear stochastic Ito-Volterra integral equations. For this purpose, we obtain stochastic operational matrix of Fibonacci functions on the finite interval [0,T]. Using these basis functions and their stochastic operational matrix, such problems can be transformed into nonlinear systems of algebraic equations which can be solved by Newton's method. Also, the existence, uniqueness and convergence of the proposed method are discussed. Furthermore, in order to show the accuracy and reliability of the proposed method, the new approach is applied to some practical problems.