numerical solution of linear stochastic differential equations driven by brownian bridg motion through the block pulse functions

 

this article is proposed a method for solving the stochastic differential equation driven brownian bridge motion by using stochastic operational matrix based on the block pulse functions and the collocation method. finally, numerical result state by using some examples. the brownian bridge (or pinned brownian motion) is a martingale, also it is gaussian process. in process have many applications in mathematical finance, biology, medical, social, scienes, etc ( see [1], [2]). in this artical, we consider the stochastic differential equation.