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Numerical Integration

  • Erich W. Schmid
  • Gerhard Spitz
  • Wolfgang Lösch

Abstract

The problem of calculating an integral numerically occurs very often in physics. If it involves a one-dimensional integration, and if the integrand is a smooth function, then no difficulties arise with the personal computer. One discretises the integrand over an equidistant mesh and applies a simple rule of integration such as the trapezoidal rule or the Simpson Rule. The required accuracy is achieved by choice of a sufficiently small mesh width.

Keywords

Legendre Polynomial Trapezoidal Rule Mesh Point Double Precision Integration Weight 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 3.1
    E. Isaacson, H.B. Keller: Analysis of Numerical Functions (John Wiley and Sons, Inc., New York 1966)Google Scholar
  2. 3.2
    A. Erdelyi, W. Magnus. F. Oberhettinger, F. Tricomi: Higher Transcendental Functions, Vols. 1 and 2 (McGraw-Hill, New York 1953)Google Scholar
  3. 3.3
    I.S. Gradshteyn, I.M. Ryzhik: Tables of Integrals, Series and Products, corrected and enlarged edition (Academic Press, New York 1980)Google Scholar
  4. 3.4
    M. Abramowitz, I.A. Stegun (eds.): Handbook of Mathematical Functions, 7th ed. (Dover Publications, New York 1970)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Erich W. Schmid
    • 1
  • Gerhard Spitz
    • 1
  • Wolfgang Lösch
    • 1
  1. 1.Institut für Theoretische PhysikUniversität TübingenTübingenFed. Rep. of Germany

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