−− A new class of multistep methods for stiff ordinary differential equations is presented. The method is based in the application of estimation functions for the derivatives and the state variables, allowing the transformation of the original system in a purely algebraic system using the solutions of previous steps. From this point of view these methods adopt a semi-implicit scheme. The novelt...

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 me...

Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrated with the constructions of new methods of weak order two, in particular, semi-implicit integrators well suited for stiff (meansquare stable...

This paper presents a sequence of deferred correction (DC) schemes built recursively from the implicit midpoint scheme for numerical solution general first order ordinary differential equations (ODEs). It is proven that each A-stable, satisfies B-convergence property, and on DC2j 2j accuracy leads to + 2 2. The guaranteed by condition. Numerical experiments with standard stiff non-stiff ODEs ar...