On error estimation in general linear methods for stiff ODEs

Authors:
J. C. Butcher;H. Podhaisky
Affiliations:
Department of Mathematics, The University of Auckland, Private Bag 92019, New Zealand;Department of Mathematics, The University of Auckland, Private Bag 92019, New Zealand
Venue:
Applied Numerical Mathematics
Year:
2006

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Abstract

This paper studies the estimation of local truncation errors for a family of general linear methods with inherent Runge-Kutta stability. While integrating with a method of order p it is possible not only to estimate the truncation error of this method but also the truncation error of the method of order p+1 asymptotically correctly. Numerical results for a variable stepsize and variable order implementation for stiff ODEs are given.