Abstract
We construct a class of cubature formulae for harmonic functions on the unit disk based on line integrals over $$2n+1$$2n+1 distinct chords. These chords are assumed to have constant distance $$t$$t to the center of the disk, and their angles to be equispaced over the interval $$[0,2\pi ]$$[0,2?]. If $$t$$t is chosen properly, these formulae integrate exactly all harmonic polynomials of degree up to $$4n+1$$4n+1, which is the highest achievable degree of precision for this class of cubature formulae. For more generally distributed chords, we introduce a class of interpolatory cubature formulae which we show to coincide with the previous formulae for the equispaced case. We give an error estimate for a particular cubature rule from this class and provide numerical examples.
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