The Runge-Kutta theory in a nutshell

SIAM Journal on Numerical Analysis

Volumn 33, Issue 5, 1996, Pages 1712-1735

  Albrecht, Peter ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

Author keywords

Embedded formulae; Existence proofs; Order conditions; Rooted trees; Rosenbrock methods; Runge Kutta methods; Stage errors

Indexed keywords

EID: 0009619039     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142994260872     Document Type: Article

References (8)

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3. R. ALEXANDER, Diagonally implicit Runge-Kutta methods for stiff O.D.E.'s, SIAM J. Numer. Anal., 14 (1977), pp. 1006-1021.
4. J. C. BUTCHER, The Numerical Analysis of Ordinary Differential Equations, Wiley, New York, 1987.
5. M. GREVE, The Treatment of Rosenbrock-Wanner Methods within a New RK-Theory, Diplomarbeit, Math. Inst., Dortmund University, 1993.
6. M. E. HOSEA, A new recurrence for computing Runge-Kutta truncation error coefficients, SIAM J. Numer. Anal., 32 (1995), pp. 1989-2001.
7. P. KAPS AND G. WANNER, A study of Rosenbrock-type methods of high order, Numer. Math., 38 (1981), pp. 279-298.
8. D. KORNMAIER, Simplifying Conditions for Fehlberg-Forms, Diplomarbeit, Math. Inst., Dortmund University, 1993.