Nordsieck representation of DIMSIMs

Numerical Algorithms

Volumn 16, Issue 2, 1997, Pages 209-230

  Butcher, J C ^a   Chartier, P ^b   Jackiewicz, Z ^c  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

^b INRIA   (France)

^c ARIZONA STATE UNIVERSITY   (United States)

Author keywords

DIMSIM methods; Error accumulation; Error estimation; Nordsieck representation; Variable step size

Indexed keywords

EID: 0141467986     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1019195215402     Document Type: Article

References (11)

1. J.C. Butcher, The Numerical Analysis of Ordinary Differential Equations (Wiley, Chichester, 1987).
2. J.C. Butcher, Diagonally-implicit multi-stage integration methods, Appl. Numer. Math. 11 (1993) 347-363.
3. J.C. Butcher, A transformation for the analysis of DIMSIMs, BIT 34 (1994) 25-32.
4. J.C. Butcher and P. Chartier, The construction of DIMSIMs for stiff ODEs and DAEs, Report Series No. 308 (The University of Auckland, New-Zealand, July 1994).
5. J.C. Butcher and Z. Jackiewicz, Diagonally implicit general linear methods for ordinary differential equations, BIT 33 (1993) 452-472.
6. J.C. Butcher and Z. Jackiewicz, Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations, Appl. Numer. Math. 21 (1996) 385-415.
7. J.C. Butcher and Z. Jackiewicz, Construction of high order DIMSIMs for ordinary differential equations, submitted.
8. J.C. Butcher and Z. Jackiewicz, Implementation of diagonally implicit multistage integration methods for ordinary differential equations, to appear in SIAM J. Numer. Anal.
9. J.C. Butcher, Z. Jackiewicz and H.D. Mittelmann, Nonlinear optimization approach to the construction of general linear methods of high order, J. Comput. Appl. Math. 81 (1997) 181-196.
10. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems (Springer, Berlin, 1991).
11. P. Lancaster and M. Tismenetsky, The Theory of Matrices (Academic Press, Orlando, 1985).