zbMATH — the first resource for mathematics

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

65L05 Numerical methods for initial value problems involving ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
PDF BibTeX Cite
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
[2] Calahan, D.A.: A stable and accurate method for the numerical integration of nonlinear systems. Proc. IEEE,56, 744 (1968)
[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
[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
[7] Hairer, E., Wanner, G.: Multistep multistage multiderivative methods for ODE’s. Computing11, 287-303 (1973) · Zbl 0271.65048
[8] Hairer, E., Wanner, G.: On the Butcher group and general multivalue methods. Computing13, 1-15 (1974) · Zbl 0293.65050
[9] Hairer, E., Wanner, G.: A theory for Nystroem methods. Numer. Math.25, 383-400 (1976) · Zbl 0307.65053
[10] Nørsett, S.P., Wanner, G.: The real-pole sandwich and oscillation equations. BIT19, 79-94 (1979) · Zbl 0413.65011
[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
[12] Gottwald, B.A., Wanner, G.: A reliable Rosenbrock integrator for stiff differential equations. Computing26, 335-360 (1981) · Zbl 0451.65056
[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)
[16] Wanner, G.: On the choice of ? for singly-implicit RK or Rosenbrock methods. BIT20, 102-106 (1980) · Zbl 0426.65026
[17] Nørsett, S.P.: One step methods of Hermite type for numerical integration of stiff systems. BIT14, 63-77 (1974) · Zbl 0278.65078
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.