Get access

Numerical resolution of linear evolution multidimensional problems of second order in time

Authors

  • B. Bujanda,

    Corresponding author
    1. Departamento de Matemática e Informática, Universidad Pública de Navarra, Campus de Arrosadía, 31006 Pamplona, Spain
    • Departamento de Matemática e Informática, Universidad Pública de Navarra, Campus de Arrosadía, 31006 Pamplona, Spain
    Search for more papers by this author
  • J. C. Jorge,

    1. Departamento de Matemática e Informática, Universidad Pública de Navarra, Campus de Arrosadía, 31006 Pamplona, Spain
    Search for more papers by this author
  • M. J. Moreta

    1. Departamento de Fundamentos del Análisis Económico I. Facultad de Ciencias Económicas y Empresariales. Universidad Complutense de Madrid. Campus de Somosaguas, Pozuelo de Alarcón, 28223 Madrid, Spain
    Search for more papers by this author

Abstract

We present a new class of efficient time integrators for solving linear evolution multidimensional problems of second-order in time named Fractional Step Runge-Kutta-Nyström methods (FSRKN). We show that these methods, combined with suitable spliting of the space differential operator and adequate space discretizations provide important advantages from the computational point of view, mainly parallelization facilities and reduction of computational complexity. In this article, we study in detail the consistency of such methods and we introduce an extension of the concept of R-stability for Runge-Kutta-Nyström methods. We also present some numerical experiments showing the unconditional convergence of a third order method of this class applied to resolve one Initial Boundary Value Problem of second order in time. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 597–620, 2012

Ancillary