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Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differential equations. (English) Zbl 0436.65047

MSC:
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L07 Numerical investigation of stability of solutions to ordinary differential equations
Software:
GEAR
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References:
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[3] Bulirsch, R., Stoer, J.: Numerical treatment of ordinary differential equations by extrapolation methods. Numer. Math.8, 1-13 (1966) · Zbl 0135.37901
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[9] Gear, C.W.: Numerical initial value problems in ordinary differential equations. N.Y.: Prentice Hall 1970
[10] Grigorieff, R.D.: Numerik gewöhnlicher Differentialgleichungen. Stuttgart: Teubner 1972 · Zbl 0249.65051
[11] Hairer, E., Wanner, G.: On the Butcher group and general mutivalue methods. Computing13, 1-15 (1974) · Zbl 0293.65050
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[13] Kaps, P.: Modifizierte Rosenbrockmethoden der Ordnung 4, 5 und 6 zur numerischen Integration steifer Differentialgleichungen. Dissertation, Universität Innsbruck, September 1977
[14] Kaps, P., Wanner, G.: Rosenbrock-type methods of high order. In press (1979) · Zbl 0469.65047
[15] Nørsett, S.P.,C-polynomials for rational approximation to the exponential function. Numer. Math.25, 39-56 (1975) · Zbl 0299.65010
[16] Nørsett, S.P., Wanner, G.: The real-pole sandwich for rational approximations and oscillation equations. BIT19, 79-94 (1979) · Zbl 0413.65011
[17] Nørsett, S.P., Wolfbrandt, A.: Order conditions for Rosenbrock-type methods. Numer. Math.32, 1-15 (1979) · Zbl 0471.65044
[18] Rosenbrock, H.H.: Some general implicit processes for the numerical solution of differential equatons. Comp. J.5, 329-331 (1963) · Zbl 0112.07805
[19] Stoer, J., Bulirsch, R.: Einführung in die Numerische Mathematik II. Berlin, Heidelberg, New York: Springer Verlag, 2. Auflage, 1978 · Zbl 0375.65001
[20] Wanner, G.: Letter to S.P. Nørsett and unpublished communications to P. Kaps and A. Wolfbrandt, 1973
[21] Wolfbrandt, A.: A study of Rosenbrock processes with respect to order conditions and stiff stability. Dissertation, Research Rep. 77.01 R, University of Göteborg, March 1977
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