Limiting precision in differential equation solvers
L. F. Shampine
Math. Comp. 28 (1974), 141-144
Math. Comp. 28 (1974), 1183.
Math. Comp. 28 (1974), 1183-1184.
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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.
F. Shampine and M.
K. Gordon, Computer solution of ordinary differential
equations, W. H. Freeman and Co., San Francisco, Calif., 1975. The
initial value problem. MR 0478627
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C. Allen Jr., Numerical computing: an introduction, W. B.
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- L. F. Shampine & M. K. Gordon, Computer Solution of Ordinary Differential Equations: Initial Value Problems, Freeman, San Francisco, 1974. MR 0478627 (57:18104)
- 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)
- L. F. Shampine & R. C. Allen, Numerical Computing: An Introduction, Saunders, Philadelphia, Pa., 1973. MR 0359250 (50:11705)
- C. W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, N.J., 1971. MR 0315898 (47:4447)
- F. T. Krogh, "On testing a subroutine for the numerical integration of ordinary differential equations," JACM. (To appear.)
- 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)
- 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)
- 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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