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Mathematics of Computation

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Step-by-step integration of $\ddot x=f(x,y,z,t)$ without a “corrector.”


Author: Samuel Herrick
Journal: Math. Comp. 5 (1951), 61-67
MSC: Primary 65.0X
DOI: https://doi.org/10.1090/S0025-5718-1951-0042795-2
MathSciNet review: 0042795
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    T. R. von Oppolzer, Lehrbuch zur Bahnbestimmung der Kometen und Planeten, v. 2, Leipzig, 1880. J. C. Watson, Theoretical Astronomy. Philadelphia, 1892. P. H. Cowell, & A. C. D. Crommelin, Investigation of the Motion of Halley’s Comet from 1759 to 1910. Appendix to Greenwich Observations for 1909. Edinburgh, 1910. p. 84. B. V. Numerov, Méthode nouvelle de la détermination des orbites et le calcul des éphémérides en tenant compte des perturbations. Observatoire Astrophysique Central de Russie, Publications, v. 2, Moscow, 1923. “A method of extrapolation of perturbations,” Roy. Astr. Soc., Monthly Notices, v. 84, 1924, p. 592-601. J. Jackson, Note on the numerical integration of $\frac {{{d^2}x}}{{d{t^2}}} = f(x,t)$. Roy. Astr. Soc., Monthly Notices, v. 84, 1924, p. 602-606. E. C. Bower, “Coefficients for interpolating a function directly from a table of double integration.” Lick Observatory, Bull., no. 445, v. 16, 1932, p. 42. Interpolation and Allied Tables, reprinted from the British Nautical Almanac for 1937, 4th edition with additions. (London, H. M. Stationery Office, 1946.) W. E. Milne, Numerical Calculus. Princeton, 1949. L. Fox & E. T. Goodwin, “Some new methods for the numerical integration of ordinary differential equations,” MS. awaiting publication.

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Article copyright: © Copyright 1951 American Mathematical Society