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

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Abstract

In this paper, we obtain stochastic operational matrix of block pulse functions on interval [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). Furthermore, the results show that the approximate solutions have a good degree of accuracy.

Keywords

Block pulse functions
Stochastic operational matrix
Stochastic Volterra–Fredholm integral equations
Itô integral
Brownian motion process

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