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The pseudo-differential approach¶to finite differences revisited

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Abstract:

We systematically derive arbitrary-order finite difference discretizations of linear (pseudo-) differential problems by appropriately approximating the symbols of the (pseudo) differential operators in frequency space. The convergence (i.e., stability and consistency) analysis of the difference schemes is based directly on micro-local properties of the exact and approximating symbols. The analytical approach presented here sheds new light on the general philosophy of finite differences.

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Authors and Affiliations

  1. Institut für Analysis und Numerik, Universität Linz, 4040 Linz, Austria, , , , , , AT

    Peter A. Markowich

  2. Laboratoire J. A. Dieudonné, UMR CNRS 6621, UNSA, Parc Valrose,¶ F-06108 Nice Cedex 2¶E-mail: poupaud@unice.fr, , , , , , FR

    Frederic Poupaud

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  1. Peter A. Markowich
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  2. Frederic Poupaud
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Received: November 1998 / Accepted: November 1998

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Markowich, P., Poupaud, F. The pseudo-differential approach¶to finite differences revisited. CALCOLO 36, 161–186 (1999). https://doi.org/10.1007/s100920050029

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  • DOI: https://doi.org/10.1007/s100920050029

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