Solving Ito integral equations with time delay via basis functions

In this paper, a direct method for solving Volterra-Fredholm integral equations with time delay by using orthogonal functions and their stochastic operational matrix of integration is proposed. Stochastic integral equations can be reduced to a sparse system which can be directly solved. Numerical examples show that the proposed scheme has a suitable degree of accuracy.

Keywords:

Delay integral equations , Stochastic operational matrix , Stochastic Volterra-Fredholm integral equations , It^o integral