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A method for numerical integration on an automatic computer

Abstract

A new method for the numerical integration of a “well-behaved” function over a finite range of argument is described. It consists essentially of expanding the integrand in a series of Chebyshev polynomials, and integrating this series term by term. Illustrative examples are given, and the method is compared with the most commonly-used alternatives, namelySimpson's rule and the method ofGauss.

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Clenshaw, C.W., Curtis, A.R. A method for numerical integration on an automatic computer. Numer. Math. 2, 197–205 (1960). https://doi.org/10.1007/BF01386223

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Keywords

  • Mathematical Method
  • Chebyshev Polynomial
  • Automatic Computer
  • Finite Range
  • Series Term