Numerical implementation a stochastic operational matrix for solving a nonlinear backward stochastic differential equation

In this paper, a computational technique is proposed for solving a nonlinear backward stochastic differential equation involving standard Brownian motion. The method is presented via the block pulse functions in combination with the collocation method. With using this approach, the nonlinear backward stochastic differential is reduced to a stochastic nonlinear system of 2m equations and 2m unknowns. Then, the error analysis is done by some preliminaries. Finally, some numerical examples demonstrate applicability and accuracy of this method.