Quadrature Rules for Unbounded Intervals and Their Application to Integral Equations

Part of the Springer Optimization and Its Applications book series (SOIA, volume 42)


Several quadrature rules for the numerical integration of smooth (nonoscillatory) functions, defined on the real (positive) semiaxis or on the real axis and decaying algebraically at infinity, are examined. Among those considered for the real axis, four alternative numerical approaches are new. The advantages and the drawbacks of each of them are pointed out through several numerical tests, either on the computation of a single integral or on the numerical solution of some integral equations.


Trapezoidal Rule Quadrature Formula Quadrature Rule Integrand Function Gaussian Formula 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Cvetković, A.S., Milovanović, G.V.: The mathematica package “Orthogonal Polynomials”, Facta Universitatis (Niš). Ser. Math. Inform. 19, 17–36 (2004)MATHGoogle Scholar
  2. 2.
    De Bonis, M.C., Mastroianni, G.: Nyström method for systems of integral equations on the real semiaxis. IMA J. Numer. Anal. 29, 632–650 (2009)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Davis, P.J., Rabinowitz, P.: Methods of numerical integration. Academic Press, New York (1984)MATHGoogle Scholar
  4. 4.
    Evans, G.A.: Some new thoughts on Gauss-Laguerre quadrature. Int. J. Comput. Math. 82, 721–730 (2005)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Gautschi, W.: Quadrature formulae on half-infinite intervals. BIT 31, 438–446 (1991)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Mastroianni, G., Milovanović, G.V.: Some numerical methods for second kind Fredholm integral equation on the real semiaxis. IMA J. Numer. Anal. 29, 1046–1066 (2009) doi:10.1093/imanum/drn056MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Mastroianni, G., Milovanović, G.V.: Interpolation processes. Basic theory and applications. Springer, Berlin (2008)MATHCrossRefGoogle Scholar
  8. 8.
    Mastroianni, G., Monegato, G.: Some new applications of truncated Gauss-Laguerre quadrature formulas. Numer. Alg. 49, 283–297 (2008) doi: 10.1007/s11075-008-9191-xMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Mori, M.: Discovery of the double exponential transformation and its developments. Publ. RIMS Kyoto Univ. 41, 897–935 (2005)MATHCrossRefGoogle Scholar
  10. 10.
    Takahasi, H., Mori, M.: Double exponential formulas for numerical integration. Publ. RIMS Kyoto Univ. 9, 721–741 (1974)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Dipartimento di MatematicaPolitecnico di TorinoTorinoItalia

Personalised recommendations