Double Exponential Integration

An excellent Numerical Integration technique used by Maple V R4 ${}^{\scriptstyle\circledRsymbol}$ (Waterloo Maple Inc.) for numerical computation of integrals.

See also Integral, Integration, Numerical Integration

References

Davis, P. J. and Rabinowitz, P. Methods of Numerical Integration, 2nd ed. New York: Academic Press, p. 214, 1984.

Di Marco, G.; Favati, P.; Lotti, G.; and Romani, F. ``Asymptotic Behaviour of Automatic Quadrature.'' J. Complexity 10, 296-340, 1994.

Mori, M. Developments in the Double Exponential Formula for Numerical Integration. Proceedings of the International Congress of Mathematicians, Kyoto 1990. New York: Springer-Verlag, pp. 1585-1594, 1991.

Mori, M. and Ooura, T. ``Double Exponential Formulas for Fourier Type Integrals with a Divergent Integrand.'' In Contributions in Numerical Mathematics (Ed. R. P. Agarwal). World Scientific Series in Applicable Analysis, Vol. 2, pp. 301-308, 1993.

Ooura, T. and Mori, M. ``The Double Exponential Formula for Oscillatory Functions over the Half Infinite Interval.'' J. Comput. Appl. Math. 38, 353-360, 1991.

Takahasi, H. and Mori, M. ``Double Exponential Formulas for Numerical Integration.'' Pub. RIMS Kyoto Univ. 9, 721-741, 1974.

Toda, H. and Ono, H. ``Some Remarks for Efficient Usage of the Double Exponential Formulas.'' Kokyuroku RIMS Kyoto Univ. 339, 74-109, 1978.