On error estimation in general linear methods for stiff ODEs

Authors:
J. C. Butcher;H. Podhaisky
Affiliations:
Department of Mathematics, The University of Auckland, New Zealand;Department of Mathematics, The University of Auckland, New Zealand
Venue:
Applied Numerical Mathematics - The third international conference on the numerical solutions of volterra and delay equations, May 2004, Tempe, AZ
Year:
2006

Citing 4
Cited 2

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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.