Weak exponential schemes for stochastic differential equations with additive noise

^** Email: cmora{at}ing-mat.udec.cl This paper develops weak exponential schemes for the numericalsolution of stochastic differential equations (SDEs) with additivenoise. In particular, this work provides first and second-ordermethods which use at each iteration the product of the exponentialof the Jacobian of the drift term with a vector. The articlealso addresses the rate of convergence of the new schemes. Moreover,numerical experiments illustrate that the numerical methodsintroduced here are a good alternative to the standard integratorsfor the long time integration of SDEs whose solutions by thecommon explicit schemes exhibit instabilities.