Numerische Mathematik

, Volume 2, Issue 1, pp 197–205 | Cite as

A method for numerical integration on an automatic computer

  • C. W. Clenshaw
  • A. R. Curtis
Article

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.

Keywords

Mathematical Method Chebyshev Polynomial Automatic Computer Finite Range Series Term 
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References

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    Hildebrand, F. B.: Introduction to numerical analysis. New York: McGraw-Hill 1956.Google Scholar
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    Longman, I. M.: Note on a method for computing infinite integrals of oscillatory functions. Proc. Cambridge Phil. Soc.52, 764–768 (1956).Google Scholar
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    Clenshaw, C. W.: The numerical solution of linear differential equations in Chebyshev series. Proc. Cambridge Phil. Soc.53, 134–149 (1957).Google Scholar
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Copyright information

© Springer-Verlag 1960

Authors and Affiliations

  • C. W. Clenshaw
    • 1
  • A. R. Curtis
    • 1
  1. 1.Mathematics DivisionNational Physical LaboratoryTeddington

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