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IMA Journal of Applied Mathematics 1979 23(2):215-222; doi:10.1093/imamat/23.2.215
© 1979 by Institute of Mathematics and its Applications
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Gauss Harmonic Interpolation Formulas for Circular Regions{dagger}

L. W. Johnson and R. D. Riess

Department of Mathematics, Virginia Polytechnic Institute Blacksburg, Virginia 24061, U.S.A.
State University Blacksburg, Virginia 24061, U.S.A.

This paper developes a procedure for computing and tabulating weights and nodes for a Gauss harmonic interpolation formula which allows one to approximate a harmonic function of two variables at a given interior point of an arbitrary circular region with given prescribed values on the boundary. The nodes can be calculated by finding the Zeros of simple, well-behaved trigonometric polynomial, and each individual weight can be calculated directly by using exactness properties. Examples are given demonstrating the ease of computation and the accuracy of the formulas.


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