On de Vogelaere's method for
Authors:
John P. Coleman and Julie Mohamed
Journal:
Math. Comp. 32 (1978), 751762
MSC:
Primary 65L05
MathSciNet review:
492036
Fulltext PDF Free Access
Abstract 
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Abstract: Easily calculated truncationerror estimates are given which permit efficient automatic error control in computations based on de Vogelaere's method. An upper bound for the local truncation error is established, the interval of absolute stability is found to be , and it is shown that the global truncation error is of order where h is the steplength.
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 S. BASAVAIAH & R. F. BROOM, "Characteristics of inline Josephson tunneling gates," IEEE Trans. Magnetics, v. MAG11, 1975, pp. 759762.
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 N. CHANDRA, "A general program to study the scattering of particles by solving coupled inhomogeneous secondorder differential equations," Computer Phys. Commun., v. 5, 1973, pp. 417429.
 [3]
 R. de VOGELAERE, "A method for the numerical integration of differential equations of second order without explicit first derivatives," J. Res. Nat. Bur. Standards, v. 54, 1955, pp. 119125. MR 0068910 (16:962g)
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 P. HENRICI, Discrete Variable Methods in Ordinary Differential Equations, Wiley, New York, 1962. MR 0135729 (24:B1772)
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 Z. KOPAL, Numerical Analysis, Chapman and Hall, London, 1955.
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 J. M. LAUNAY, "Bodyfixed formulation of rotational excitation: exact and centrifugal decoupling results for CO  He," J. Phys. B: A tom. Molec. Phys., v. 9, 1976, pp. 18231838.
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 W. A. LESTER, JR., "De Vogelaere's method for the numerical integration of secondorder differential equations without explicit first derivatives: application to coupled equations arising from the Schrödinger equation," J. Computational Phys., v. 3, 1968, pp. 322326.
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 R. E. SCRATON, "The numerical solution of secondorder differential equations not containing the first derivative explicitly," Comput. J., v. 6, 1964, pp. 368370. MR 0158545 (28:1768)
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 L. F. SHAMPINE, H. A. WATTS & S. M. DAVENPORT, "Solving nonstiff ordinary differential equationsthe state of the art," SIAM Rev., v. 18, 1976, pp. 376411. MR 0413522 (54:1636)
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 L. VERLET, "Computer 'experiments' on classical fluids. I. Thermodynamical properties of LennardJones molecules," Phys. Rev., v. 159, 1967, pp. 98103.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197804920366
PII:
S 00255718(1978)04920366
Article copyright:
© Copyright 1978
American Mathematical Society
