Abstract
In [1] there is an expansion in Bernoulli polynomials for sufficiently smooth real functions in an interval [a,b]⊂R that has useful applications to numerical analysis. An analogous result in a 2-dimensional context is derived in [2] in the case of rectangle. In this note we generalize the above-mentioned one-dimensional expansion to the case of C m-functions on a 2-dimensional simplex; a method to generalize the expansion on an N-dimensional simplex is also discussed. This new expansion is applied to find new cubature formulas for 2-dimensional simplex.
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References
F. Costabile, Expansions of real functions in Bernoulli polynomials and applications, Conf. Sem. Univ. Bari 273 (1999).
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Costabile, F., Dell'Accio, F. Expansions over a Simplex of Real Functions by Means of Bernoulli Polynomials. Numerical Algorithms 28, 63–86 (2001). https://doi.org/10.1023/A:1014074211736
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DOI: https://doi.org/10.1023/A:1014074211736