On the implementation of ESIRK methods for stiff IVPs

Numerical Algorithms

Volumn 26, Issue 3, 2001, Pages 201-218

  Butcher, J C ^a   Chen, D J L ^b  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

^b LING TUNG UNIVERSITY   (Taiwan)

Author keywords

Effective order; Error estimate; Predictor; Simply implicit Runge Kutta methods; Variable stepsize

Indexed keywords

EID: 0035588495     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1016607621405     Document Type: Article

References (11)

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3. J.C. Butcher and P. Chartier, A generalization of singly-implicit Runge-Kutta methods, Appl. Numer. Math. 24 (1997) 343-350.
4. J.C. Butcher and P. Chartier, The effective order of singly-implicit Runge-Kutta methods, Numer. Algorithms 20 (1999) 269-284.
5. J.C. Butcher and D.J.L. Chen, ESIRK methods and variable stepsize, Appl. Numer. Math. 28 (1998) 193-207.
6. D.J.L. Chen, The effective order of singly-implicit methods for stiff differential equations, Ph.D. thesis, The University of Auckland (1998).
7. 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).
8. K. Gustafsson, Control of error and convergence in ODE solvers, Ph.D. thesis, Lund Institute of Technology, Sweden (1993).
9. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II, Stiff and Differential-Algebraic Problems (Springer, Berlin, 1987).
10. A. Hindmarsh, A Systematized Collection of ODE Solvers (North-Holland, Amsterdam, 1983).
11. S.P. Nørsett and P.G. Thomsen, Local error control in SDIRK-methods, BIT 26 (1986) 100-13.