Energy and momentum conserving methods of arbitrary order for the numerical integration of equations of motion. II: Motion of a system of particles. (English) Zbl 0382.65031

LaBudde, Robert A.; Greenspan, Donald

Numer. Math. 26, 1-16 (1976).

MSC:

65L05

Numerical methods for initial value problems involving ordinary differential equations

References:

[1]	For a survey of pertinent topics, see: Hirschfelder, J. O., Curtiss, C. F., Bird, R. B.: Molecular Theory of Gases and Liquids, Wiley, N. Y., 1965; · Zbl 0057.23402
[2]	Tolman, R. C.: The Principles of Statistical Mechanics, Oxford: Oxford University Press 1938 · Zbl 0019.35902
[3]	For reviews, see: Bunker, D. L.: Classical Trajectory Methods. Methods of Computational Physics, vol. 10, p. 287, N. Y.: Academic Press 1971;
[4]	LaBudde, R. A.: Classical Mechanics of Molecular Collisions University of Wisconsin Theoretical Chemistry Institute Report WIS-TC1-414 (1973)
[5]	See, e. g.: Roy, A. E.: Foundations of Astrodynamics, N. Y.: MacMillan, 1965;
[6]	Chebotarev, G. A.: Analytical and Numerical, Methods of Celestial Mechanics. N. Y.: American Elsevier Publishing Co., 1967 · Zbl 0166.42705
[7]	See, e. g., the review by: Duncombe, R. L., Seidelmann, P. K., Klepczynski, W. J.: Dynamical Astronomy of the Solar System. Ann. Rev. of Astron. and Astrophys.11, 135 (1973)
[8]	LaBudde, R. A., Greenspan, D.: Discrete Mechanics ? A General Treatment: J. Computational Physics15, 134 (1974). · Zbl 0301.70006
[9]	LaBudde, R. A., Greenspan, D.: Discrete Mechanics ? A General Treatment: University of Wisconsin, Computer Sciences Department Report WIS-CS-192 (1973) · Zbl 0301.70006
[10]	LaBudde, R. A., Greenspan, D.: Discrete Mechanics for Anisotropic Potentials. University of Wisconsin, Computer Sciences Department Report WIS-CS-203 (1974) · Zbl 0301.70006
[11]	LaBudde, R. A., Greenspan, D.: Discrete Mechanics for Nonseparable Potentials with Application to the LEPS form. University of Wisconsin Computer Sciences Department Report WIS-CS-210 (1974) · Zbl 0301.70006
[12]	LaBudde, R. A., Greenspan, D.: Energy and Angular Momentum Conserving Methods of Arbitrary Order for the Numerical Integration of Equations of Motion. I. Motion of a Single Particle. University of Wisconsin Computer Sciences Department Report WIS-CS-208 (1974) · Zbl 0364.65066
[13]	LaBudde, R. A., Greenspan, D.: Energy and Momentum Conserving Methods of Arbitrary Order for the Numerical Integration of Equations of Motion. II. Motion of a System of Particles. University of Wisconsin Computer Sciences Department Report WIS-CS-215 (1974) · Zbl 0382.65031
[14]	See, e. g.: Nordsieck, A.: Numerical Solution of Ordinary Differential Equations. Math. Comp.16, 22 (1962); · Zbl 0105.31902
[15]	Gear, C. W.: Numerical, Initial Value Problems in Ordinary Differential Equations, Sect. 9.2.5. Englewood Cliffs, N. J.: Prentice-Hall, 1971; · Zbl 1145.65316
[16]	LaBudde, R. A.: Extension of Nordsieck’s Methods to the Numerical Solution of Higher-Order Ordinary Differential Equations. University of Wisconsin Theoretical Chemistry Institute Report WIS-TC1-443 (1971)