Stabilized starting algorithms for collocation Runge-Kutta methods

Computers and Mathematics with Applications

Volumn 45, Issue 1-3, 2003, Pages 411-428

  Gonzalez Pinto S ^a   Montijano, J I ^b   Perez Rodriguez S ^a  

^a UNIVERSIDAD DE LA LAGUNA   (Spain)

^b UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

Implicit Runge Kutta methods; Starting algorithms; Stiff initial value problems

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; INTEGRATION; ITERATIVE METHODS; LINEAR SYSTEMS; PROBLEM SOLVING;

STARTING ALGORITHMS;

RUNGE KUTTA METHODS;

EID: 0037287485     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(03)80027-5     Document Type: Article

References (10)

1. S. Gonzalez-Pinto, J.I. Montijano and S. Pérez-Rodriguez, On the starting algorithms for fully implicit Runge-Kutta methods, BIT (to appear).
2. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II, Springer-Verlag, Berlin, (1996).
3. J. Sand, Starting methods for the iteration of IRK's, Dept. of Computer Science, Univ. Copenhagen, Denmark, (1989).
4. A. Prothero and A. Robinson, On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations, Math. Comp. 28, 145-162, (1974).
5. K. Dekker and J.G. Verwer, Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations, North-Holland, Amsterdam, (1984).
6. S. Gonzalez-Pinto, J.I. Montijano and L. Randez, Iterative schemes for implicit Runge-Kutta methods, Appl. Numer. Math. 17, 363-382, (1995).
7. M.N. Spijker, On the error committed by stopping the Newton iteration in implicit Runge-Kutta methods, Annals. of Numer. Math. 1, 199-212, (1994).
8. W.M. Lioen, J.J.B. deSwart and W.A. van der Veen, Test set for IVP solvers, http://www.cwi.nl/cwi/projects/IVPtestset.sthtml, (1996).
9. W.H. Enright, T.E. Hull and B. Lindberg, Comparing numerical methods for stiff systems of ODEs, BIT 15, 10-48, (1975).
10. H. Olsson and G. Söderlind, Stage value predictors and efficient Newton iterations in implicit Range- Kutta methods, SIAM Journal on Scientific Computing 20 (1), 185-202, (1999).