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A new approach for the construction of high order A-stable explicitintegrators for ordinary differential equations (ODEs) is theoreticallystudied. Basically, the integrators are obtained by splitting, at each timestep, the solution of the original equation in two parts: the solution of alinear ordinary differential equation plus the solution of an auxiliary ODE.The first one is solved by a Local Linearization scheme in such a way thatA-stability is ensured, while the second one can be approximated by any extantscheme, preferably a high order explicit Runge-Kutta scheme. Results on theconvergence and dynamical properties of this new class of schemes are given, aswell as some hints for their efficient numerical implementation. An specificscheme of this new class is derived in detail, and its performance is comparedwith some Matlab codes in the integration of a variety of ODEs representingdifferent types of dynamics.

Local Linearization-Runge Kutta Methods: a class of A-stable explicit integrators for dynamical systems