Abstract:
We give new algorithms for computing the complete elliptic integrals of the first and second kinds and some related functions. The algorithms are constructed on the base of rapidly converging power series; the fixed sign of the series guarantees their good conditionality (stability with respect to rounding errors). The algorithms turned out to be flexible and easily adaptable to any specific demands of computing practice.
Keywords:
complete elliptic integrals of the first and second kinds, toroidal functions, conical functions.
Citation:
V. N. Belykh, “Algorithms for computing complete elliptic integrals and some related functions”, Sib. Zh. Ind. Mat., 15:2 (2012), 21–32; J. Appl. Industr. Math., 6:4 (2012), 410–420
\Bibitem{Bel12}
\by V.~N.~Belykh
\paper Algorithms for computing complete elliptic integrals and some related functions
\jour Sib. Zh. Ind. Mat.
\yr 2012
\vol 15
\issue 2
\pages 21--32
\mathnet{http://mi.mathnet.ru/sjim722}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3098823}
\transl
\jour J. Appl. Industr. Math.
\yr 2012
\vol 6
\issue 4
\pages 410--420
\crossref{https://doi.org/10.1134/S1990478912040023}
Linking options:
https://www.mathnet.ru/eng/sjim722
https://www.mathnet.ru/eng/sjim/v15/i2/p21
This publication is cited in the following 4 articles:
V. N. Belykh, “Nenasyschaemye algoritmy chislennogo resheniya ellipticheskikh kraevykh zadach v gladkikh osesimmetrichnykh oblastyakh”, Matem. tr., 25:1 (2022), 3–50
V. N. Belykh, “Superconvergent algorithms for the numerical solution of the Laplace equation in smooth axisymmetric domains”, Comput. Math. Math. Phys., 60:4 (2020), 545–557
V. N. Belykh, Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy, 2020, 13
V. N. Belykh, “K probleme chislennoi realizatsii integralnykh operatorov osesimmetrichnykh kraevykh zadach (algoritmy bez nasyscheniya)”, Ufimsk. matem. zhurn., 4:4 (2012), 22–37
Citation in format AMSBIB
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