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Summation by Parts Operators for Finite Difference Approximations of Second-Derivatives with Variable Coefficients

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An Erratum to this article was published on 31 December 2011

Abstract

Finite difference operators approximating second derivatives with variable coefficients and satisfying a summation-by-parts rule have been derived for the second-, fourth- and sixth-order case by using the symbolic mathematics software Maple. The operators are based on the same norms as the corresponding approximations of the first derivative, which makes the construction of stable approximations to general multi-dimensional hyperbolic-parabolic problems straightforward.

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Authors and Affiliations

  1. Uppsala University, Uppsala, Finland

    Ken Mattsson

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  1. Ken Mattsson
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Correspondence to Ken Mattsson.

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Mattsson, K. Summation by Parts Operators for Finite Difference Approximations of Second-Derivatives with Variable Coefficients. J Sci Comput 51, 650–682 (2012). https://doi.org/10.1007/s10915-011-9525-z

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  • DOI: https://doi.org/10.1007/s10915-011-9525-z

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