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Second derivative methods with RK stability

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Abstract

General linear methods are extended to the case in which second derivatives, as well as first derivatives, can be calculated. Methods are constructed of third and fourth order which are A-stable, possess the Runge–Kutta stability property and have a diagonally implicit structure for efficient implementation.

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Authors and Affiliations

  1. Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, New Zealand

    J. C. Butcher

  2. Faculty of Mathematical science, Tabriz University, Tabriz, Iran

    G. Hojjati

Authors
  1. J. C. Butcher
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  2. G. Hojjati
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Corresponding author

Correspondence to G. Hojjati.

Additional information

Communicated by C. Brezinski

AMS subject classification

65L05

G. Hojjati: Corresponding author.

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Butcher, J.C., Hojjati, G. Second derivative methods with RK stability. Numer Algor 40, 415–429 (2005). https://doi.org/10.1007/s11075-005-0413-1

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  • DOI: https://doi.org/10.1007/s11075-005-0413-1

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