Application of new basis functions for solving nonlinear stochastic differential equations

This paper presents an approach for solving nonlinear stochastic differential equations (nsdes) using a new basis functions (nbfs). these functions and their operational matrices are used for representing matrix form of the nbfs. with using this method in combination with the collocation method, the nsdes are reduced a stochastic nonlinear system of 2m + 2 equations and 2m + 2 unknowns. then, the error analysis is proved. finally, numerical examples illustrate applicability and accuracy of the presented method.