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On the implementation of implicit Runge-Kutta methods

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Abstract

The modified Newton iterations in the implementation of ans stage implicit Runge-Kutta method for ann dimensional differential equation system require 2s 3 n 3/3+O(n 2) operations for theLU factorisations and 2s 2 n 2+O(n) operations for the back substitutions. This paper describes a method for transforming the linear system so as to reduce these operation counts.

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References

  1. J. C. Butcher,Implicit Runge-Kutta Processes, Math. Comp. 18 (1964), 50–64.

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  2. S. P. Nørsett,Semi Explicit Runge-Kutta Methods, Mathematics Department, University of Trondheim, Reprint No. 6/74.

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Authors and Affiliations

  1. Department of Mathematics, The University of Auckland, Auckland, New Zealand

    J. C. Butcher

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  1. J. C. Butcher
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Butcher, J.C. On the implementation of implicit Runge-Kutta methods. BIT 16, 237–240 (1976). https://doi.org/10.1007/BF01932265

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  • DOI: https://doi.org/10.1007/BF01932265

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