Error propagation of general linear methods for ordinary differential equations

Authors:
J. C. Butcher;Z. Jackiewicz;W. M. Wright
Affiliations:
Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, New Zealand;Department of Mathematics, Arizona State University, Tempe, Arizona 85287, USA;Department of Mathematical and Statistical Sciences, La Trobe University, Melbourne, Vic. 3086, Australia
Venue:
Journal of Complexity
Year:
2007

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Abstract

We discuss error propagation for general linear methods for ordinary differential equations up to terms of order p+2, where p is the order of the method. These results are then applied to the estimation of local discretization errors for methods of order p and for the adjacent order p+1. The results of numerical experiments confirm the reliability of these estimates. This research has applications in the design of robust stepsize and order changing strategies for algorithms based on general linear methods.