Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations
A. Abdulle, G. Vilmart and K.C. Zygalakis
Abstract. We introduce two drift-diagonally-implicit and derivative-free integrators for stiff systems of Itô 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 [K. Debrabant and A. Rößler, Appl. Num. Math., 59, 2009].
Key Words.Stiff SDEs, drift-implicit stochastic methods, mean-square stability.