Abstract: “In this paper, an efficient method to determine a numerical solution of a stochastic nonlinear differential equation (SNDE) is proposed. The method is illustrated by using a stochastic operational matrix based on the triangular functions (TFs). In this proposed method, the SNDE is reduced to a stochastic nonlinear system of equations and unknowns. Then, the error analysis is demonstrated by using some preliminaries. Finally, the method is evaluated with some numerical examples.”

Keywords: Triangular functions, Standard Brownian motion, Stochastic operational matrix, Stochastic nonlinear differential equations, Collocation method