Estimating the Global Error of Runge-Kutta Approximations for Ordinary Differential Equations

  • K. Dekker
  • J. G. Verwer
Part of the International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique book series (ISNM, volume 62)


The user of a code for solving the initial value problem for ordinary differential systems is normally left with the difficult task of assessing the accuracy of the numerical result returned by the code. Even when the code reports an estimate of the global error, the question may remain whether this estimate is correct, i. e. whether the user can rely on the estimate. This paper proposes a simple idea of measuring the reliability of the global error estimate with the aim of assisting the user in the validation of the numerical result. The idea is put into practice with the existing code GERK (ACM Algorithm 504) developed by Shampine and Watts. This code uses global Richardson extrapolation for the error estimation, which in many cases can also be applied to Runge-Kutta codes for delay equations.


Coarse Grid Global Error Stiff Problem Parallel Integration Local Error Estimation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Basel AG 1983

Authors and Affiliations

  • K. Dekker
    • 1
  • J. G. Verwer
    • 1
  1. 1.Mathematisch CentrumAmsterdamThe Netherlands

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