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Better software for ODEs. (English) Zbl 0415.65039

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
68Q60 Specification and verification (program logics, model checking, etc.)
68Q25 Analysis of algorithms and problem complexity
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References:

[1] IMSL: International Mathematical and Statistical Libraries, Inc., Houston, Texas.; IMSL: International Mathematical and Statistical Libraries, Inc., Houston, Texas.
[2] Bulirsch, R.; Stoer, J., Numerical treatment of ordinary differential equations by extrapolation methods, Numer. Math., 8, 1-13 (1966) · Zbl 0135.37901
[3] Hull, T. E.; Enright, W. H.; Jackson, K. R., User’s guide for DVERK—a subroutine for solving non-stiff ODE’s (1976), Comp. Sci. Dept. Rept. 100: Comp. Sci. Dept. Rept. 100 Toronto, Canada
[4] Gear, C. W., The automatic integration of ordinary differential equations, CACM, 14, 176-179 (1971) · Zbl 0217.21701
[5] Shampine, L. F.; Gordon, M. K., Computer Solution of Ordinary Differential Equations: the Initial Value Problem (1975), Freeman: Freeman San Francisco · Zbl 0347.65001
[6] Shampine, L. F.; Watts, H. A., The art of writing a Runge-Kutta code, Appl. Math. & Comp., 5, 93-121 (1979), Part II · Zbl 0431.68039
[7] Shampine, L. F.; Wisniewski, J. A., The variable order Runge-Kutta code RKSW and its performance (1978), Sandia Laboratories Rept. SAND78-1347: Sandia Laboratories Rept. SAND78-1347 Albuquerque, NM
[8] Gladwell, I., Initial value routines in the NAG Library (3-5 April 1979), University of Illinois: University of Illinois Champaign, Presentation made to the SIGNUM conference on Numerical Ordinary Differential Equations
[9] Hull, T. E.; Enright, W. H.; Fellen, B. M.; Sedgwick, A. E., Comparing numerical methods for ordinary differential equations, SIAM J. Numer. Anal., 9, 602-637 (1972) · Zbl 0221.65115
[10] Jackson, K. R.; Enright, W. H.; Hull, T. E., A theoretical criterion for comparing Runge-Kutta formulas, SIAM J. Numer. Anal., 15, 618-641 (1978) · Zbl 0391.65030
[11] Shampine, L. F., Limiting precision in differential equation solvers, Math. Comp., 28, 141-144 (1974) · Zbl 0273.65063
[12] Shampine, L. F., Limiting precision in differential equation solvers—II. Sources of trouble and starting a code, Math. Comp., 32, 1115-1122 (1978) · Zbl 0387.65045
[13] Shampine, L. F.; Watts, H. A.; Davenport, S. M., Solving nonstiff ordinary differential equations—the state of the art, SIAM Rev., 18, 376-411 (1976) · Zbl 0349.65042
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