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Explicit Nordsieck methods with quadratic stability

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Abstract

We describe the construction of explicit Nordsieck methods with s stages of order p = s − 1 and stage order q = p with inherent quadratic stability and quadratic stability with large regions of absolute stability. Stability regions of these methods compare favorably with stability regions of corresponding general linear methods of the same order with inherent Runge–Kutta stability.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Salerno, via Ponte don Melillo, 84084, Fisciano (Sa), Italy

    Angelamaria Cardone

  2. Department of Mathematics, Arizona State University, Tempe, AZ, 85287, USA

    Zdzislaw Jackiewicz

  3. AGH University of Science and Technology, Kraków, Poland

    Zdzislaw Jackiewicz

Authors
  1. Angelamaria Cardone
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  2. Zdzislaw Jackiewicz
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Correspondence to Angelamaria Cardone.

Additional information

The work of Z. Jackiewicz was partially supported by the National Science Foundation under grant NSF DMS–0509597.

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Cardone, A., Jackiewicz, Z. Explicit Nordsieck methods with quadratic stability. Numer Algor 60, 1–25 (2012). https://doi.org/10.1007/s11075-011-9509-y

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  • DOI: https://doi.org/10.1007/s11075-011-9509-y

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