Abstract
The multidimensional Itô–Volterra integral equations arise in many problems such as an exponential population growth model with several independent white noise sources. In this paper, we obtain a stochastic operational matrix of block pulse functions on interval [ 0 , 1 ) to solve m-dimensional stochastic Itô–Volterra integral equations. By using block pulse functions and their stochastic operational matrix of integration, m -dimensional stochastic Itô–Volterra integral equations 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 ) . Furthermore, a 95% confidence interval of the errors’ mean is made, the results shows that the approximate solutions have a credible degree of accuracy.
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