DESIRE: Diagonally extended singly implicit Runge-Kutta effective order methods

Numerical Algorithms

Volumn 17, Issue 1-2, 1998, Pages 121-145

  Butcher, J C ^a   Diamantakis, M T ^b  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Effective order; Implicit Runge Kutta methods; Singly implicit methods

Indexed keywords

EID: 0032388654     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1011623226983     Document Type: Article

References (17)

1. R. Alexander, Diagonally implicit Runge-Kutta methods for stiff ODEs, SIAM J. Numer. Anal. 14 (1977) 1006-1021.
2. K. Burrage, A special family of Runge-Kutta methods for solving stiff differential equations, BIT 18 (1978) 22-41.
3. K. Burrage, J.C. Butcher and F.H. Chipman, An implementation of singly-implicit Runge-Kutta methods, BIT 20 (1980) 326-340.
4. J.C. Butcher, The effective order of Runge-Kutta methods, in: Conference on the Numerical Solution of Differential Equations, Dundee (Springer, Berlin, 1969) pp. 133-139.
5. J.C. Butcher, On the implementation of implicit Runge-Kutta methods, BIT 16 (1976) 237-240.
6. J.C. Butcher, A transformed implicit Runge-Kutta method, J. Assoc. Comput. Mach. 26 (1979) 731-738.
7. J.C. Butcher, Towards efficient implementation of singly-implicit methods, ACM Trans. Math. Software 14 (1988) 68-75.
8. J.C. Butcher and J.R. Cash, Towards efficient Runge-Kutta methods for stiff systems, SIAM J. Numer. Anal. 27 (1990) 753-761.
9. J.C. Butcher, J.R. Cash and M.T. Diamantakis, DESI methods for stiff initial value problems, ACM Trans. Math. Software 22 (1996) 401-422.
10. J.C. Butcher and P. Chartier, A generalization of singly-implicit Runge-Kutta methods, Volterra centennial, Tempe, AZ (1996), Appl. Numer. Math. 24 (1997) 343-350.
11. J.C. Butcher and P. Chartier, The effective order of singly-implicit Runge-Kutta methods, in preparation.
12. J.C. Butcher and D.J.L. Chen, ESIRK methods and variable stepsize, in preparation.
13. J.R. Cash and M.T. Diamantakis, On the implementation of block Runge-Kutta methods for stiff IVPs, in: Scientific Computation and Differential Equations, Auckland (1993), Ann. Numer. Math. 1 (1994) 385-398.
14. M.T. Diamantakis, Diagonally extended singly implicit Runge-Kutta methods for stiff initial value problems, Ph.D. thesis, Imperial College, University of London, UK (1995).
15. M.T. Diamantakis, The NUMOL solution of time-dependent PDEs using DESI Runge-Kutta formulae, in: Numerical Methods for Ordinary Differential Equations, Atlanta, GA (1994), Appl. Numer. Math. 17 (1995) 235-249.
16. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II. Stiff and Differential Algebraic Problems, Springer Series in Computational Mathematics 14 (Springer, Berlin, 2nd ed., 1996).
17. P. Kaps, Rosenbrock-type methods, in: Proceedings on Numerical Methods for Stiff Initial Value Problems, eds. G. Dalhquist and R. Jeltschs, Oberwolfach, Germany (Institut für Geometrie und Praktische Mathematik, RWTH Aachen, 1981).