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A study of Rosenbrock-type methods of high order. (English) Zbl 0469.65047

65L05Initial value problems for ODE (numerical methods)
65L20Stability and convergence of numerical methods for ODE
Full Text: DOI EuDML
[1] Rosenbrock, H.H.: Some general implicit processes for the num, solution of differential equations. Comput. J.5, 329-331 (1963) · Zbl 0112.07805 · doi:10.1093/comjnl/5.4.329
[2] Calahan, D.A.: A stable and accurate method for the numerical integration of nonlinear systems. Proc. IEEE,56, 744 (1968) · doi:10.1109/PROC.1968.6367
[3] van der Houwen, P.J.: Construction of integration formulas for initial value problems. Amsterdam: North Holland 1977 · Zbl 0359.65057
[4] Wolfbrandt, A.: A study of Rosenbrock processes with respect to order conditions and stiff stability. Thesis, Göteborg 1977 · Zbl 0371.41007
[5] Nørsett S.P., Wolfbrandt, A.: Order conditions for Rosenbrock type methods. Numer. Math.32, 1-15 (1979) · Zbl 0471.65044 · doi:10.1007/BF01397646
[6] Kaps, P., Rentrop, P.: Generalized Runge Kutta methods of order four with step size control for stiff ODE’s. Numer. Math.33, 55-68 (1979) · Zbl 0436.65047 · doi:10.1007/BF01396495
[7] Hairer, E., Wanner, G.: Multistep multistage multiderivative methods for ODE’s. Computing11, 287-303 (1973) · Zbl 0271.65048 · doi:10.1007/BF02252917
[8] Hairer, E., Wanner, G.: On the Butcher group and general multivalue methods. Computing13, 1-15 (1974) · Zbl 0293.65050 · doi:10.1007/BF02268387
[9] Hairer, E., Wanner, G.: A theory for Nystroem methods. Numer. Math.25, 383-400 (1976) · Zbl 0307.65053 · doi:10.1007/BF01396335
[10] Nørsett, S.P., Wanner, G.: The real-pole sandwich and oscillation equations. BIT19, 79-94 (1979) · Zbl 0413.65011 · doi:10.1007/BF01931224
[11] Enright, W.H. Hull, T.E., Lindberg, B.: Comparing numerical methods for stiff systems of ODE’s. BIT15, 10-48 (1975) · Zbl 0301.65040 · doi:10.1007/BF01932994
[12] Gottwald, B.A., Wanner, G.: A reliable Rosenbrock integrator for stiff differential equations. Computing26, 335-360 (1981) · Zbl 0451.65056 · doi:10.1007/BF02237954
[13] Wanner, G.: On the integration of stiff differential equations, ISNM 37. (J. Descloux and J. Marti eds.) Basel: Birkhäuser 1977 · Zbl 0361.65071
[14] Kaps, P.: Modifizierte Rosenbrockmethoden der Ordnungen4, 5 and 6 zur numerischen Integration steifer Differentialgleichungen, Dissertation Innsbruck 1977
[15] Chan, Y.N.I., Birnbaum, I., Lapidus, L.: Solution of stiff differential equations and the use of imbedding techniques. Industr. and Engin. Chemistry Fundamentals,17, 133-148 (1978) · doi:10.1021/i160067a001
[16] Wanner, G.: On the choice of ? for singly-implicit RK or Rosenbrock methods. BIT20, 102-106 (1980) · Zbl 0426.65026 · doi:10.1007/BF01933591
[17] Nørsett, S.P.: One step methods of Hermite type for numerical integration of stiff systems. BIT14, 63-77 (1974) · Zbl 0278.65078 · doi:10.1007/BF01933119