Starting algorithms for IRK methods

Journal of Computational and Applied Mathematics

Volumn 83, Issue 2, 1997, Pages 269-288

  Laburta, M P ^a  

^a UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

Implicit methods; Maximum order; Runge Kutta; Starting algorithms

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; BOUNDARY VALUE PROBLEMS; COMPUTATIONAL METHODS; DIFFERENTIAL EQUATIONS; FUNCTION EVALUATION;

RUNGE KUTTA METHOD;

ITERATIVE METHODS;

EID: 0031558498     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(97)00112-X     Document Type: Article

References (10)

1. K. Burrage, J.C. Butcher, F.H. Chipman, An implementation of singly diagonally implicit Runge-Kutta methods, BIT 20 (1980) 326-340.
2. R.P.K. Chan, Generalized symmetric Runge-Kutta methods, Computing 50 (1) (1993) 31-49.
3. S. González-Pinto, J.I. Montijano, L. Rández, Iterative schemes for three-stage implicit Runge-Kutta methods, Appl. Numer. Math. 17 (1995) 363-382.
4. E. Hairer, S.P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems, Springer, Berlin, 1987.
5. E. Hairer, G. Wanner, Solving Ordinary Differential Equations II, Stiff and Differential-Algebraic Problems, Springer, Berlin, 1991.
6. S.P. Norsett, P.G. Thomsen, Local error control in SDIRK-methods, BIT 26 (1986) 100-113.
7. S.P. Norsett, G. Wanner, Perturbed collocation and Runge-Kutta methods, Numer. Math. 38 (1981) 193-208.
8. J. Sand, Starting methods for the iteration of IRK's, Dept. of Computer Science, Univ. Copenhagen, Denmark, 1989.
9. J.M. Sanz-Serna, Runge-Kutta schemes for Hamiltonian systems, BIT 28 (1988) 877-883.
10. J.M. Sanz-Serna, M.P. Calvo, Numerical Hamiltonian Problems, Chapman & Hall, London, 1994.