Numerical approach for solving stochastic Volterra–Fredholm integral equations by stochastic operational matrix

In this paper, we obtain stochastic operational matrix of block pulse functions on interval [0,1)[0,1) to solve stochastic Volterra–Fredholm integral equations. By using block pulse functions and their stochastic operational matrix of integration, the stochastic Volterra–Fredholm integral equation can be reduced to a linear lower triangular system which can be directly solved by forward substitution. We prove that the rate of convergence is O(h)O(h). Furthermore, the results show that the approximate solutions have a good degree of accuracy.