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Instructive experiments with some Runge-Kutta-Rosenbrock methods. (English) Zbl 0481.65037

MSC:
65L05 Numerical methods for initial value problems involving ordinary differential equations
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[1] Rosenbrock, H.H., Some general implicit processes for the numerical solution of differential equations, Computer J., 5, 329-330, (1963) · Zbl 0112.07805
[2] Verwer, J.G., An analysis of rosenbrock methods for non-linear stiff initial value problems, SIAM J. numer. anal., (1982), to appear · Zbl 0478.65045
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[6] Griepentrog, E., Numerische integration stiefer differentialgleichungs-systeme mit einschrittverfahren, Beiträge zur numerischen Mathematik, 8, 59-74, (1980) · Zbl 0436.65051
[7] Kreiss, H.O., Difference methods for stiff ordinary differential equations, SIAM J. numer. anal., 15, 21-58, (1978) · Zbl 0385.65035
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[9] Kaps, P.; Wanner, G., A study of rosenbrock type methods of high order, Numer. math., 38, 297-298, (1981) · Zbl 0469.65047
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[11] Kaps, P.; Rentrop, P., Generalized Runge-Kutta methods of order 4 with stepsize control for stiff ordinary differential equations, Numer. math., 33, 55-68, (1979) · Zbl 0436.65047
[12] B. A. Gottwald and G. Wanner, Stiff systems of ordinary differential equations in biology and chemistry: Validation of numerical methods for their solution. In Continuous Simulation of Physical Systems (Edited by T. D. Bui), to appear.
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