An efficient spectral method for the numerical solution to stochastic differential equations

International audienceWe consider a new approach for the numerical approximation of stochastic differential equations driven by white noise. The proposed method shares some features with the stochastic collocation techniques and, in particular, it takes advantage of the assumption of smoothness of the functional to be approximated, to achieve fast convergence. The solution to the stochastic differential equation is represented by means of Lagrange polynomials. The coefficients of the polynomial basis are functions of time and they can be computed by solving a system of deterministic ordinary differential equations. Numerical examples are presented to illustrate the accuracy and the efficiency of the proposed method