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Shampine, Lawrence F.

Local error control in codes for ordinary differential equations. (English) Zbl 0362.65066

Appl. Math. Comput. 3, 189-210 (1977).
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scan of Zbl 0362.65066

Cited in 12 Documents

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
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References:

[1] Shampine, L. F.; Gordon, M. K., Computer Solution of Ordinary Differential Equations: the Initial Value Problem (1975), Freeman: Freeman San Francisco · Zbl 0347.65001
[2] Birkhoff, G.; Rota, G.-C., Ordinary Differential Equations (1962), Ginn: Ginn New York · Zbl 0183.35601
[3] Stewart, N. F., An integration routine using a Runge-Kutta method, M. Sc. Thesis (1965), Dept. of Comput. Sci., Univ. of Toronto
[4] Shampine, L. F.; Allen, R. C., Numerical Computing: an Introduction (1973), Saunders: Saunders Philadelphia · Zbl 0266.65001
[5] Gear, C. W., Numerical Initial Value Problems in Ordinary Differential Equations (1971), Prentice-Hall: Prentice-Hall Englewood Cliffs, N.J · Zbl 0217.21701
[6] Zonneveld, J. A., Automatic Numerical Integration, Math. Centre Tracts No. 8 (1964), Mathematisch Centrum: Mathematisch Centrum Amsterdam · Zbl 0139.31901
[7] Krogh, F. T., vodq/svdq/dvdq—Variable order integrators for the numerical solution of ordinary differential equations, TU Doc. No. CP-2308, NPO-11643 (May 1969), Jet Propul. Lab: Jet Propul. Lab Pasadena, Calif
[8] Henrici, P., Discrete Variable Methods in Ordinary Differential Equations (1962), Wiley: Wiley New York · Zbl 0112.34901
[9] Lefschetz, S., Differential Equations: Geometric Theory (1957), Interscience: Interscience New York · Zbl 0080.06401
[10] Gabel, G. F., A predictor-corrector method using divided differences, M. Sc. Thesis (1965), Dept. of Comput. Sci., Univ. of Toronto
[11] Hull, T. E.; Enright, W. H.; Fellen, B. M.; Sedgwick, A. E., Comparing numerical methods for ordinary differential equations, SIAM. J. Numer. Anal., 9, 603-637 (1972) · Zbl 0221.65115
[12] Enright, W. H.; Bedet, R.; Farkas, I.; Hull, T. E., Test results on initial value methods for non-stiff ordinary differential equations, Tech. Rept. No. 68 (1974), Dept. of Comput. Sci., Univ. of Toronto
[13] Krogh, F. T., On testing a subroutine for the numerical integration of ordinary differential equations, JACM, 20, 545-562 (1973) · Zbl 0292.65039
[14] Fox, P. A.; Rice, J., desub:integration of a first-order system of ordinary differential equations, Mathematical Software (1971), Academic: Academic New York, Chapter 9
[15] Shampine, L. F., Stiffness and non-stiff differential equation solvers, (Collatz, L., Numerische Behandlung von Differentialgleichungen, ISNM 27 (1975), Birkhäuser: Birkhäuser Basel), 287-301 · Zbl 0303.65065
[16] Shampine, L. F., Local extrapolation in the solution of ordinary differential equations, Math. Comput., 27, 91-97 (1973) · Zbl 0254.65052
[17] Krogh, F. T., Changing step size in the integration of differential equations using modified divided differences, Proc. of the Conf. on the Numer. Solution of Ordinary Differential Equations (1974), Springer: Springer New York, Lecture Notes in Math. No. 362 · Zbl 0279.65059
[18] Krogh, F. T., The numerical integration of stiff differential equations, TRW Rep. No. 99900-6573-R000 (1968), Redondo Beach, Calif.
[19] Shampine, L. F.; Watts, H. A.; Davenport, S. M., Solving non-stiff ordinary differential equations—the state of the art, SIAM Rev., 18, 376-411 (1976) · Zbl 0349.65042
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