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ARK methods up to order five

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Abstract

Almost Runge–Kutta methods (or “ARK methods”) have many of the advantages of Runge–Kutta methods but, for many problems, are capable of greater accuracy. In this paper a complete classification of fourth order ARK methods with 4 stages is presented. The paper also analyzes fifth order methods with 5 or with 6 stages. Some limited numerical experiments show that the new methods are capable of excellent performance, comparable to that of known highly efficient Runge–Kutta methods.

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Authors and Affiliations

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

    J.C. Butcher

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  1. J.C. Butcher
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Butcher, J. ARK methods up to order five. Numerical Algorithms 17, 193–221 (1998). https://doi.org/10.1023/A:1016640625396

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  • DOI: https://doi.org/10.1023/A:1016640625396

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