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Conditions for the coefficients of Runge-Kutta methods for systems of n-th order differential equations

By H.-M. Hebsaker

Abstract

AbstractTo derive order conditions for Runge-Kutta methods of Nyström or Fehlberg type, applicable to arbitrary order differential equations, a theory similar to that about Runge-Kutta methods for first order systems, due to Butcher [1], is developed. By a new definition of elementary differentials, which is independent of the order of the given system, each condition to be satisfied by the coefficients of the method directly follows from the representation of the corresponding elementary differential

Publisher: Published by Elsevier B.V.
Year: 1982
DOI identifier: 10.1016/0771-050X(82)90001-8
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