Second weak order explicit stabilized methods for stiff
stochastic differential equations
A. Abdulle, G. Vilmart and K.C. Zygalakis
Abstract. We introduce a new family of explicit integrators for stiff Itô stochastic differential equations
(SDEs) of weak order two. These numerical methods belong to the class of one-step
stabilized methods with extended stability domains and do not suffer from the stepsize reduction
faced by standard explicit methods. The family is based on the standard second order
orthogonal Runge-Kutta Chebyshev methods (ROCK2) for deterministic problems. The
convergence, and the mean-square and asymptotic stability properties of the methods are
analyzed. Numerical experiments, including applications to nonlinear SDEs and parabolic
stochastic partial differential equations are presented and confirm the theoretical results.
Key Words. Stiff SDEs, explicit stochastic methods, stabilized methods, orthogonal Runge-Kutta Chebyshev, S-ROCK.