A numerical method for solving m-dimensional stochastic Ito-Volterra integral equations by stochastic operational matrix

作者：Maleknejad K^*; Khodabin M; Rostami M

来源：Computers & Mathematics with Applications, 2012, 63(1): 133-143.

DOI：10.1016/j.camwa.2011.10.079

• Block pulse functions
• Stochastic operational matrix
• Stochastic Ito-Volterra integral equations
• Ito integral
• Brownian motion process

The multidimensional Ito-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 Ito-Volterra integral equations. By using block pulse functions and their stochastic operational matrix of integration, m-dimensional stochastic Ito-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.

• 出版日期2012-1