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An algorithm for Gauss harmonic formulas

  • Part II Numerical Mathematics
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Abstract

LetD be an open, bounded, simply-connected region inR 2 with boundaryB. Let (x*,y*) be an arbitrary point ofD. This paper constructs an algorithm for computing Gauss harmonic formulas forD and the point (x*,y*). Such formulas approximate a harmonic function at (x*,y*) in terms of a linear combination of its boundary values. Such formulas are useful for approximating the solution of the Dirichlet problem, especially when the problem is to be solved many times at the same point with different boundary values.

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Authors and Affiliations

  1. Department of Mathematics, George Mason University, 22030, Fairfax, Virginia, USA

    J. Chen

  2. Department of Mathematics, Virginia Polytechnic Institute & State University, 24061, Blacksburg, Virginia, USA

    L. W. Johnson & R. D. Riess

Authors
  1. J. Chen
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  2. L. W. Johnson
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  3. R. D. Riess
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Chen, J., Johnson, L.W. & Riess, R.D. An algorithm for Gauss harmonic formulas. BIT 24, 78–84 (1984). https://doi.org/10.1007/BF01934517

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  • DOI: https://doi.org/10.1007/BF01934517

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