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

This paper presents a new numerical technique for solving stochastic Ito integral equations. A new operational matrix for integration of cardinal Legendre polynomials are introduced. By using this nexw operational matrix of integration and the so called collocation method, stochastic nonlinear integral equations are reduced to systems of algebraic equations with unknown coefficients. Only small dimension of Legendre operational matrix is needed to obtain a satisfactory results. Some error estimations are provided and illustrative examples are also included to demonstrate the efficiency of the new technisue.