Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff ito stochastic differential equations Mean-square A-stable diagonally drift-implicit integrators of weak

摘要

We introduce two drift-diagonally-implicit and derivative-free integrators for stiff systems of Ito stochastic differential equations with general non-commutative noise which have weak order 2 and deterministic order 2, 3, respectively. The methods are shown to be mean-square A-stable for the usual complex scalar linear test problem with multiplicative noise and improve significantly the stability properties of the drift-diagonally-implicit methods previously introduced (Debrabant and RoeBler, Appl. Numer. Math. 59(3-4):595-607, 2009).