Approximation solution of two-dimensional linear stochastic Volterra-Fredholm integral equation via two-dimensional Block-pulse ‎functions

Subject Areas : International Journal of Industrial Mathematics

M. Fallahpour‎‎ ¹ , M. Khodabin‎ ² , K. Maleknejad‎ ³

1 - Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
2 - Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
3 - Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.

Received: 2016-11-17 Accepted : 2016-11-17 Published : 2016-11-01

Keywords: Block-pulse function, Two-dimensional equation, Stochastic integral equation, Volterra-fredholm integral, Operational matrix, Brownian motion process, Ito ‎integral,

Abstract :

In this paper, a numerical efficient method based on two-dimensional block-pulse functions (BPFs) is proposed to approximate a solution of the two-dimensional linear stochastic Volterra-Fredholm integral equation. Finally the accuracy of this method will be shown by an example.