Symmetric runge-kutta methods with higher derivatives and quadratic extrapolation

  • Authors:

  • Gennady Yu. Kulikov;Ekaterina Yu. Khrustaleva;Arkadi I. Merkulov

  • Affiliations:

  • School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa;Ulyanovsk State University, Ulyanovsk, Russia;Ulyanovsk State University, Ulyanovsk, Russia

  • Venue:
  • ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part I
  • Year:
  • 2006

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Abstract

In this paper we study the symmetry of Runge-Kutta methods with higher derivatives. We find conditions which provide this property for the above numerical methods. We prove that the family of E-methods constructed earlier consists of symmetric methods only, which lead to the quadratic extrapolation technique in practice.