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Numerical evaluation of a symmetric potential function

Author(s): Lori A. Carmack.
Journal: Math. Comp. 67 (1998), 641-646.
MSC (1991): Primary 31B99, 65D30, 76C99
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Abstract: We discuss the numerical evaluation of a symmetric potential function which arises naturally in applications. We present a method designed to accurately and efficiently compute this integral, and compare the performance of this method with two other popular techniques. This method requires considerably fewer function evaluations than all other techniques we tested, and is applicable to any integral which can be expressed in terms of complete elliptic integrals.

References:

1.: M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, Dover Publications, Inc., New York, 1965. MR 34:8606
2.: B. C. Carlson, ``Numerical computation of real or complex elliptic integrals," Numer. Algorithms 10 (1995), no. 1-2, 13-26. MR 97h:33035
3.: IMSL Sfun/Library Users Manual (IMSL Inc., 2500 CityWest Boulevard, Houston, TX 77042).
4.: NAG Fortran Library (Numerical Algorithms Group, 256 Banbury Road, Oxford OX27DE, U. K. ), Chapter S.
5.: R. Piessens, et. al., QUADPACK, Springer-Verlag Berlin, New York, 1983. MR 85b:65022


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