Explicit stabilized integration of stiff determinisitic or stochastic problems

Explicit stabilized methods for stiff ordinary differential equations have a long history. Proposed in the early 1960s and developed during 40 years for the integration of stiff ordinary differential equations, these methods have recently been extended to implicit-explicit or partitioned type methods for advection-diffusion-reaction problems, and to efficient explicit solvers for stiff mean-square stable stochastic problems. After a short review on the basic stabilized methods we discuss some recent developments.