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Stability of implicit multiderivative deferred correction methods

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Abstract

Very recently, a novel class of parallelizable high-order time discretization schemes has been introduced in Schütz et al. (J Sci Comput 90(54):1–33, 2022). In this current work, we analyze the stability properties of those schemes and introduce a small but effective modification which only necessitates minor modifications of existing implementations. It is shown how this modification leads to A(\(\alpha \))-stable schemes with \(\alpha \) being close to \(90^{\circ }\). Numerical examples illustrate an additional favorable influence of this modification on the accuracy of those schemes.

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Acknowledgements

J. Zeifang was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Project No. 457811052. D. Seal was funded by the Office of Naval Research, Grant Number N0001419WX01523 and N0001420WX00219. The computing resources and services used in this work were provided by the VSC (Flemish Supercomputer Center), funded by the Research Foundation—Flanders (FWO) and the Flemish Government.

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Authors and Affiliations

  1. Faculty of Sciences and Data Science Institute, Universiteit Hasselt, Agoralaan Gebouw D, 3590, Diepenbeek, Belgium

    Jonas Zeifang & Jochen Schütz

  2. Department of Mathematics, United States Naval Academy, 572C Holloway Road, Annapolis, MD, 21402, USA

    David C. Seal

Authors
  1. Jonas Zeifang
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  2. Jochen Schütz
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  3. David C. Seal
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Correspondence to Jonas Zeifang.

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Communicated by Christian Lubich.

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Zeifang, J., Schütz, J. & Seal, D.C. Stability of implicit multiderivative deferred correction methods. Bit Numer Math 62, 1487–1503 (2022). https://doi.org/10.1007/s10543-022-00919-x

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