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A Parallel Algorithm for the Estimation of the Global Error in Runge–Kutta Methods

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Abstract

The object of this work is the estimate of the global error in the numerical solution of the IVP for a system of ODE's. Given a Runge–Kutta formula of order q, which yields an approximation y n to the true value y(x n ), a general, parallel method is presented, that provides a second value y n * of order q+2; the global error e n =y n −y(x n ) is then estimated by the difference y n −y n *. The numerical tests reported, show the very good performance of the procedure proposed. A comparison with the code GEM90 is also appended.

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Authors and Affiliations

  1. Department of Biotechnology and Bioscience, University of Milano, Bicocca, Piazza della Scienza 2, 20126, Milano, Italy

    R. Tirani

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  1. R. Tirani
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Tirani, R. A Parallel Algorithm for the Estimation of the Global Error in Runge–Kutta Methods. Numerical Algorithms 31, 311–318 (2002). https://doi.org/10.1023/A:1021199921217

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