legendre cardinal functions and their applications in solving nonlinear stochastic differential equations

This paper presents a new numerical technique for solving stochastic itô integral equations. a new operational matrix for integration of cardinal legendre polynomials are introduced. by using this new operational matrix of integration and the so-called collocation method, stochastic nonlinear itô integral equations are reduced to systems of algebraic equations with unknown coefficients. only small dimension of legnedre operational matrix is needed to obtain a satisfactory results. some error estimations are provided and illustrative examples are also included to demonstrate the efficiency and applicability of the proposed numerical technique.