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Variable stepsize continuous two-step Runge-Kutta methods for ordinary differential equations

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Abstract

A general class of variable stepsize continuous two-step Runge-Kutta methods is investigated. These methods depend on stage values at two consecutive steps. The general convergence and order criteria are derived and examples of methods of orderp and stage orderq=p orq=p−1 are given forp≤5. Numerical examples are presented which demonstrate that high order and high stage order are preserved on nonuniform meshes with large variations in ratios between consecutive stepsizes.

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Authors and Affiliations

  1. Department of Mathematics, Arizona State University, 85287-1804, Tempe, AZ, USA

    Z. Jackiewicz & S. Tracogna

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  1. Z. Jackiewicz
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  2. S. Tracogna
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Additional information

Communicated by J.C. Butcher

The work of the first author was supported by the National Science Foundation under grant NSF DMS-9208048. The work of the second author was supported by the Italian Government.

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Jackiewicz, Z., Tracogna, S. Variable stepsize continuous two-step Runge-Kutta methods for ordinary differential equations. Numer Algor 12, 347–368 (1996). https://doi.org/10.1007/BF02142812

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  • DOI: https://doi.org/10.1007/BF02142812

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