Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



On de Vogelaere's method for $ y\sp{\prime\prime}=f(x,\,y)$

Authors: John P. Coleman and Julie Mohamed
Journal: Math. Comp. 32 (1978), 751-762
MSC: Primary 65L05
MathSciNet review: 492036
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Easily calculated truncation-error 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 $ [ - 2,0]$, and it is shown that the global truncation error is of order $ {h^4}$ where h is the steplength.

References [Enhancements On Off] (What's this?)

  • [1] S. BASAVAIAH & R. F. BROOM, "Characteristics of in-line Josephson tunneling gates," IEEE Trans. Magnetics, v. MAG-11, 1975, pp. 759-762.
  • [2] N. CHANDRA, "A general program to study the scattering of particles by solving coupled inhomogeneous second-order differential equations," Computer Phys. Commun., v. 5, 1973, pp. 417-429.
  • [3] Rene de Vogelaere, A method for the numerical integration of differential equations of second order without explicit first derivatives, J. Res. Nat. Bur. Standards 54 (1955), 119–125. MR 0068910
  • [4] Peter Henrici, Discrete variable methods in ordinary differential equations, John Wiley & Sons, Inc., New York-London, 1962. MR 0135729
  • [5] Z. KOPAL, Numerical Analysis, Chapman and Hall, London, 1955.
  • [6] J. D. Lambert, Computational methods in ordinary differential equations, John Wiley & Sons, London-New York-Sydney, 1973. Introductory Mathematics for Scientists and Engineers. MR 0423815
  • [7] J. D. Lambert, The initial value problem for ordinary differential equations, The state of the art in numerical analysis (Proc. Conf., Univ. York, Heslington, 1976) Academic Press, London, 1977, pp. 451–500. MR 0458896
  • [8] J. -M. LAUNAY, "Body-fixed formulation of rotational excitation: exact and centrifugal decoupling results for CO - He," J. Phys. B: A tom. Molec. Phys., v. 9, 1976, pp. 1823-1838.
  • [9] 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. 322-326.
  • [10] R. E. Scraton, The numerical solution of second-order differential equations not containing the first derivative explicitly, Comput. J. 6 (1963/1964), 368–370. MR 0158545
  • [11] L. F. Shampine, H. A. Watts, and S. M. Davenport, Solving nonstiff ordinary differential equations—the state of the art, SIAM Rev. 18 (1976), no. 3, 376–411. MR 0413522
  • [12] L. VERLET, "Computer 'experiments' on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules," Phys. Rev., v. 159, 1967, pp. 98-103.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65L05

Retrieve articles in all journals with MSC: 65L05

Additional Information

Article copyright: © Copyright 1978 American Mathematical Society