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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


Limiting precision in differential equation solvers

Author: L. F. Shampine
Journal: Math. Comp. 28 (1974), 141-144
MSC: Primary 68A05
Corrigendum: Math. Comp. 28 (1974), 1183.
Corrigendum: Math. Comp. 28 (1974), 1183-1184.
MathSciNet review: 0329308
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Abstract | References | Similar Articles | Additional Information

Abstract: Machine dependent limits on the step size and local error tolerance are discussed. By taking them into account codes can be made more robust.

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

  • [1] L. F. Shampine & M. K. Gordon, Computer Solution of Ordinary Differential Equations: Initial Value Problems, Freeman, San Francisco, 1974. MR 0478627 (57:18104)
  • [2] F. T. Krogh, VODG/SVDQ/DVDQ--Variable Order Integrators for the Numerical Solution of Ordinary Differential Equations, TU Doc. No. CP-2308, NPO-11643, May 1969, Jet Propulsion Laboratory, Pasadena, California. MR 0261790 (41:6402)
  • [3] L. F. Shampine & R. C. Allen, Numerical Computing: An Introduction, Saunders, Philadelphia, Pa., 1973. MR 0359250 (50:11705)
  • [4] C. W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, N.J., 1971. MR 0315898 (47:4447)
  • [5] F. T. Krogh, "On testing a subroutine for the numerical integration of ordinary differential equations," JACM. (To appear.)
  • [6] F. T. Krogh, Changing Stepsize in the Integration of Differential Equations Using Modified Divided Differences, Proc. Conference on the Numerical Solution of Ordinary Differential Equations (Austin, Texas, Oct. 1972), Lecture Notes in Math., Springer-Verlag. (To appear.) MR 0362908 (50:15346)
  • [7] E. Vitasek, The Numerical Stability in Solution of Differential Equations, Proc. Conf. Numerical Solution of Differential Equations (Dundee, Scotland, 1969), Springer, Berlin, 1969, pp. 87-111. MR 42 #2681. MR 0267779 (42:2681)
  • [8] E. K. Blum, "A modification of the Runge-Kutta fourth-order method," Math. Comp., v. 16, 1962, pp. 176-187. MR 26 #3190. MR 0145661 (26:3190)

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Additional Information

PII: S 0025-5718(1974)0329308-8
Keywords: Limiting precision, local error, minimum step size, robust software, roundoff
Article copyright: © Copyright 1974 American Mathematical Society

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