On the derivation of explicit two-step peer methods

• Autores: Manuel Calvo Pinilla , Juan Ignacio Montijano Torcal , Luis Rández García , M. Van Daele
• Localización: Applied numerical mathematics, ISSN-e 0168-9274, Vol. 61, Nº. 4, 2011, págs. 395-409
• Idioma: inglés
• DOI: 10.1016/j.apnum.2010.11.004
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• Resumen

  • 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.