JournalsprimsVol. 9 , No. 3DOI 10.2977/prims/1195192451

Double Exponential Formulas for Numerical Integration

  • Hidetosi Takahasi

    University of Tokyo, Japan
  • Masatake Mori

    Tokyo Denki University, Japan
Double Exponential Formulas for Numerical Integration cover

Abstract

A family of numerical quadrature formulas is introduced by application of the trapezoidal rule to infinite integrals which result from the given integrals  ∫ ba f(x)dx by suitable variable transformations x = ø(u). These formulas are characterized by having double exponential asymptotic behavior of the integrands in the resulting infinite integrals as u → ± ∞, and it is shown both analytically and numerically that such formulas are generally optimal with respect to the ecomony of the number of sampling points.