Approximate solution of the stochastic Volterra integral equations via expansion method

Subject Areas : International Journal of Industrial Mathematics

M. Khodabin ¹ , K. Maleknejad ² , T. Damercheli 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: 2013-11-18 Accepted : 2013-11-18 Published : 2014-12-01

Keywords: Taylor series expansion, Stochastic Volterra integral e, Itˆo integral,

Abstract :

In this paper, we present an efficient method for determining the solution of the stochastic second kind Volterra integral equations (SVIE) by using the Taylor expansion method. This method transforms the SVIE to a linear stochastic ordinary differential equation which needs specified boundary conditions. For determining boundary conditions, we use the integration technique. This technique gives an approximate simple and closed form solution for the SVIE. Expectation of the approximating process is computed. Some numerical examples are used to illustrate the accuracy of the method.