  A new approach for the construction of high order A-stable explicit
integrators for ordinary differential equations (ODEs) is theoretically
studied. Basically, the integrators are obtained by splitting, at each time
step, the solution of the original equation in two parts: the solution of a
linear ordinary differential equation plus the solution of an auxiliary ODE.
The first one is solved by a Local Linearization scheme in such a way that
A-stability is ensured, while the second one can be approximated by any extant
scheme, preferably a high order explicit Runge-Kutta scheme. Results on the
convergence and dynamical properties of this new class of schemes are given, as
well as some hints for their efficient numerical implementation. An specific
scheme of this new class is derived in detail, and its performance is compared
with some Matlab codes in the integration of a variety of ODEs representing
different types of dynamics.
