The zeros of regular Coulomb wave functions and of their derivatives
HTML articles powered by AMS MathViewer
- by Yasuhiko Ikebe PDF
- Math. Comp. 29 (1975), 878-887 Request permission
Abstract:
A simple and efficient numerical method for computing the zeros of regular Coulomb wave functions and of their derivatives is presented. The method is based on the characterization of the zeros of the functions and of their derivatives in terms of eigenvalues of certain compact matrix operators. A similar approach has been reported for the computation of the zeros of Bessel functions and of their derivatives [9], [14].References
- Milton Abramowitz and Irene A. Stegun (eds.), Handbook of mathematical functions, with formulas, graphs, and mathematical tables, Dover Publications, Inc., New York, 1966. MR 0208797
- W. J. Cody and K. E. Hillstrom, Chebyshev approximations for the Coulomb phase shift, Math. Comp. 24 (1970), 671–677. MR 273785, DOI 10.1090/S0025-5718-1970-0273785-4 W. J. CODY & KATHLEEN A. PACIOREK, "Remark on algorithm 292-regular Coulomb wave functions," Comm. ACM, v. 13, 1970, p. 573.
- A. R. Curtis, Coulomb wave functions, Royal Society Mathematical Tables, Vol. 11, Published for the Royal Society at the Cambridge University Press, New York, 1964. Prepared under the direction of The Coulomb Wave Functions Panel of the Mathematical Tables Committee. MR 0167643 W. GAUTSCHI, "Algorithm 292-regular Coulomb wave functions," Comm. ACM, v. 9, 1966, pp. 793-795. W. GAUTSCHI, "Remark on algorithm 292-regular Coulomb wave functions," Comm. ACM, v. 12, 1969, p. 280.
- Walter Gautschi, Computational aspects of three-term recurrence relations, SIAM Rev. 9 (1967), 24–82. MR 213062, DOI 10.1137/1009002
- Walter Gautschi, An application of minimal solutions of three-term recurrences to Coulomb wave functions, Aequationes Math. 2 (1969), 171–176. MR 246512, DOI 10.1007/BF01817701
- J. Grad and E. Zakrajšek, Method for evaluation of zeros of Bessel functions, J. Inst. Math. Appl. 11 (1973), 57–72. MR 331725, DOI 10.1093/imamat/11.1.57 J. H. GUNN, "Algorithm 300-Coulomb wave functions," Comm. ACM, v. 10, 1967, pp. 244-245. K. S. KÖLBIG, "Certification of algorithm 300-Coulomb wave functions," Comm. ACM, v. 12, 1969, pp. 279-280. K. S. KÖLBIG, "Certification algorithm 292-regular Coulomb wave functions," Comm. ACM, v. 12, 1969, pp. 278-279. K. S. KÖLBIG, "Remarks on the computation of Coulomb wave functions," Computer Physics Comm., v. 4, 1972, pp. 214-220. Y. IKEBE, The Zeros of Bessel Functions and of Their Derivatives, Technical Report CNA-81, Center for Numerical Analysis, The University of Texas, Austin, Texas, February 1974. M. A. KRASNOSEL’SKIĬ, G. M. VAĬNIKKO, P. P. ZABREĬKO, Ja. B. RUTICKIĬ & V. Ja. STECENKO, Approximate Solution of Operator Equations, "Nauka", Moscow, 1969; English transl., Wolters-Noordhoff, Groningen, 1972. MR 41 #4271. B. T. SMITH, J. M. BOYLE, B. S. GARBOW, Y. IKEBE, C. KLEMA & C. B. MOLER, Matrix Eigensystem Routines—EISPACK Guide, Springer-Verlag, New York, 1974.
- A. J. Strecok and J. A. Gregory, High precision evaluation of the irregular Coulomb wave functions, Math. Comp. 26 (1972). MR 314239, DOI 10.1090/S0025-5718-1972-0314239-8
- J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965. MR 0184422
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Math. Comp. 29 (1975), 878-887
- MSC: Primary 65D20
- DOI: https://doi.org/10.1090/S0025-5718-1975-0378361-5
- MathSciNet review: 0378361