@article{5fc92f1aa35e4d899c687950efbcc745,
title = "Error propagation of general linear methods for ordinary differential equations",
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.",
keywords = "Adaptive stepsize selection, Error propagation, General linear methods, Local error estimation for methods of adjacent orders, Nordsieck representation, Stability analysis",
author = "Butcher, {J. C.} and Zdzislaw Jackiewicz and Wright, {W. M.}",
note = "Funding Information: One of the authors (Z.J.) acknowledges support from the Foundation under Grant DMS-0509597. Another (W.M.W.) was supported by the Royal Society of New Zealand. Each of the authors (especially J.C.B.) acknowledge assistance and support from the Marsden Fund. The helpful and constructive comments by the referees have led to substantial improvements; the authors gratefully acknowledge this assistance. Funding Information: Keywords: General linear methods; Nordsieck representation; Error propagation; Local error estimation for methods of adjacent orders; Adaptive stepsize selection; Stability analysis ∗Corresponding author. E-mail addresses: butcher@math.auckland.ac.nz (J.C. Butcher), jackiewi@math.la.asu.edu (Z. Jackiewicz), w.wright@latrobe.edu.au (W.M. Wright). URLs: http://www.math.auckland.ac.nz/butcher/ (J.C. Butcher), http://math.la.asu.edu/jackiewi/zdzislaw.html (Z. Jackiewicz), http://www.latrobe.edu.au/mathstats/staff/wright/ (W.M. Wright). 1The research of this author was supported by the New Zealand Marsden Fund. 2The research of this author was supported by the National Science Foundation under Grant DMS-0509597. 3The research of this author was supported by a New Zealand Science and Technology Postdoctoral Fellowship.",
year = "2007",
doi = "10.1016/j.jco.2007.01.009",
language = "English (US)",
volume = "23",
pages = "560--580",
journal = "Journal of Complexity",
issn = "0885-064X",
publisher = "Academic Press Inc.",
number = "4-6",
}