Resumen de On the derivation of explicit two-step peer methods
Manuel Calvo Pinilla, Juan Ignacio Montijano Torcal, Luis Rández García, M. Van Daele
The so-called two-step peer methods for the numerical solution of Initial Value Problems (IVP) in differential systems were introduced by R. Weiner, B.A. Schmitt and coworkers as a tool to solve different types of IVPs either in sequential or parallel computers. These methods combine the advantages of Runge�Kutta (RK) and multistep methods to obtain high stage order and therefore provide in a natural way a dense output. In particular, several explicit peer methods have been proved to be competitive with standard RK methods in a wide selection of non-stiff test problems.
The aim of this paper is to propose an alternative procedure to construct families of explicit two step peer methods in which the available parameters appear in a transparent way. This allows us to obtain families of fixed stepsize s stage methods with stage order 2s-1, which provide dense output without extra cost, depending on some free parameters that can be selected taking into account the stability properties and leading error terms. A study of the extension of these methods to variable stepsize is also carried out. Optimal s stage methods with s=2,3 are derived.
