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Stability analysis of the Crank–Nicolson-Leapfrog method with the Robert–Asselin–Williams time filter

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Abstract

Geophysical flow simulations have evolved sophisticated implicit–explicit time stepping methods (based on fast-slow wave splittings) followed by time filters to control any unstable models that result. Time filters are modular and parallel. Their effect on stability of the overall process has been tested in numerous simulations. In this paper, we study the stability of the Crank–Nicolson-Leapfrog scheme with the Robert–Asselin–Williams time filter.

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Notes

  1. Thus, we assume \(\nu \in (0,1]\) throughout the text.

  2. For detailed proof, see the expanded version at http://www.mathematics.pitt.edu/sites/default/files/research-pdfs/CNLFraw.

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Authors and Affiliations

  1. Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA , 15260, USA

    Nicholas Hurl, William Layton, Yong Li & Catalin Trenchea

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  1. Nicholas Hurl
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  2. William Layton
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  3. Yong Li
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  4. Catalin Trenchea
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Corresponding author

Correspondence to Catalin Trenchea.

Additional information

Communicated by Mechthild Thalhammer.

Partially supported by the Air Force under grant FA9550-12-1-0191 and the NSF under grant DMS 1216465.

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Hurl, N., Layton, W., Li, Y. et al. Stability analysis of the Crank–Nicolson-Leapfrog method with the Robert–Asselin–Williams time filter. Bit Numer Math 54, 1009–1021 (2014). https://doi.org/10.1007/s10543-014-0493-1

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  • DOI: https://doi.org/10.1007/s10543-014-0493-1

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