Numerical solution for stochastic Volterra-Fredholm integral equations with delay arguments

Abstract

We present a method for computing the stochastic operational matrix of integration to advance the study of stochastic Volterra-Fredholm integral equations (SVFIEs) based on delay arguments. First, the method evaluates the combined effects of the delay and its parameters on the accuracy improvement of the convergence rate. Our results can be applied to SVFIEs, with the operational delay matrices of the block pulse function simplified to algebraic ones. Numerical calculations were performed on a PC using Python 3 programs. Results also demonstrate the accuracy of approximate solutions; arithmetic operations are carried out without the need for derivation or integration.

Keywords

• stochastic Volterra-Fredholm integral equations
• block-pulse functions
• Itô integral
• delay operational matrix
• error analysis