A MULTIDIMENSIONAL ANALOGUE OF THE SIMPSON'S FORMULA OF INTEGRAL

DOI10.1142/S0219887810004294zbMATH Open1200.41033arXiv0908.3533OpenAlexW2083508611MaRDI QIDQ3569297

Kazuyuki Fujii

Publication date: 18 June 2010

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

Abstract: The Simpson's formula is obtained by approximating the integral of a function on some interval by the integral of the quadratic polynomial determined by the function. However, a multidimensional analogue of the formula has not been given as far as we know. In this paper such a formula is given. Our formula is simple and beautiful, so it may be convenient in Mathematics or Mathematical Physics.

Full work available at URL: https://arxiv.org/abs/0908.3533

zbMATH Keywords

Simpson's formulageneralized Simpson's formula

Mathematics Subject Classification ID

Multidimensional problems (41A63) Approximate quadratures (41A55)

Related Items (3)

A formula connecting the Young and Pollard integrals ⋮ J. Simons' type integral formula for hypersurfaces in a unit sphere ⋮ The modified Simpson's rule for line integrals

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