On the numerical solution of stiff IVPs by Lobatto IIIA Runge-Kutta methods

Journal of Computational and Applied Mathematics

Volumn 82, Issue 1-2, 1997, Pages 129-148

  Pinto, S González ^a   Rodríguez, S Pérez ^a   Torcal, J I Montijano ^b  

^a UNIVERSIDAD DE LA LAGUNA   (Spain)

^b UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

Iterative schemes; Lobatto IIIA formulae; Runge Kutta methods; Stiff problems

Indexed keywords

APPROXIMATION THEORY; ITERATIVE METHODS; PROBLEM SOLVING;

RUNGE KUTTA METHODS; STIFF INITIAL VALUE PROBLEMS;

DIFFERENTIAL EQUATIONS;

EID: 0031232991     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0377-0427(97)00086-1     Document Type: Article

References (18)

1. U. Ascher, On symmetric schemes and differential-algebraic equations, SIAM J . Sci. Statist. Comput. 10 (5) (1989) 937-949.
2. T.A. Bickart, An efficient solution process for implicit Runge-Kutta methods, SIAM J. Numer Anal. 14 (1977) 1022-1027.
3. K. Burrage, J.C. Butcher, F.H. Chipman, An implementation of singly implicit Runge-Kutta methods, BIT20 (1980) 326-340.
4. J.C. Butcher, On the implementation of implicit Runge-Kutta methods, BIT 16 (1976) 237-240.
5. J.C. Butcher, Some implementation schemes for implicit Runge-Kutta methods, Proc. Dundee Conf. on Numerical Analysis, 1979, Lecture Notes in Math, Vol. 773, Springer, Berlin, 1980, pp. 12-24.
6. J.C. Butcher, The Numerical Analysis of Ordinary Differential Equations, Wiley, Chichester, 1987.
7. G.D. Byrne, A.C. Hindmarsh, A. polyalgorithm for the numerical solution of ordinary differential equations, ACM Trans. Math. Soft. 1 (1975) 71-96.
8. M. Calvo, S. González-Pinto, J.I. Montijano, Runge-Kutta methods for the numerical solution of stiff semilinear initial value problems, to be published.
9. M. Calvo, S. González-Pinto, J.I. Montijano, Convergence of Runge-Kutta methods for stiff nonlinear differential equations, to be published.
10. G.J. Cooper, J.C. Butcher, An iteration scheme for implicit Runge-Kutta method, IMA J. Numer. Anal. 3 (1983) 127-140.
11. G.J. Copper, R. Vignesvaran, A scheme for the implementation of implicit Runge-Kutta methods, Computing 45 (1990) 321-332.
12. K. Dekker, J.G. Verwer, Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations, North-Holland, Amsterdam, 1984.
13. S. Gonzalez-Pinto, C. Gonzalez-Concepcion, J.I. Montijano, Iterative schemes for Gauss methods, Comput. Math. Appl. 27 (7) (1994) 67-81.
14. S. Gonzalez-Pinto, J.I. Montijano, L. Randez, Iterative schemes for three-stage implicit Runge-Kutta methods, Appl. Numer. Math. 17 (1995) 363-382.
15. E. Hairer, Ch. Lubich, M. Roche, The numerical solution of differential algebraic systems by Runge-Kutta methods, Lecture Notes in Math, Vol. 1049, Springer, Berlin, 1989.
16. E. Hairer, G. Wanner, Solving Ordinary Differential Equations II, Springer, Berlin, 1991.
17. J.D. Lambert, Numerical Methods for Ordinary Differential Systems, Wiley, New York, 1991.
18. A. Prothero, A. Robinson, On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations, Math. Comp. 28 (1974) 145-162.