The construction of practical general linear methods

BIT Numerical Mathematics

Volumn 43, Issue 4, 2003, Pages 695-721

  Butcher, J C ^a   Wright, W M ^a  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

General linear methods; Inherent Runge Kutta stability

Indexed keywords

EID: 4043179733     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:BITN.0000009952.71388.23     Document Type: Article

References (10)

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3. J. C. Butcher, General linear methods for stiff differential equations, BIT, 41 (2001), pp. 240-264.
4. J. C. Butcher and P. Chartier, The effective order of singly-implicit Runge-Kutta methods, Numer. Algorithms, 20 (1999), pp. 269-284.
5. J. C. Butcher and Z. Jackiewicz, A reliable error estimation for diagonally implicit multistage integration methods, BIT, 41 (2001), pp. 656-665.
6. J. C. Butcher and W. M. Wright, A transformation relating explicit and diagonally-implicit general linear methods, Appl. Numer. Math., 44 (2003), pp. 313-327.
7. C. W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, 1971.
8. A. Nordsieck, On numerical integration of differential equations, Math. Comp., 16 (1963), pp. 22-49.
9. W. M. Wright, Explicit general linear methods with inherent Runge-Kutta stability, Numer. Algorithms, 31 (2002), pp. 381-399.
10. W. M. Wright, General linear methods with inherent Runge-Kutta stability, Ph.D. thesis, Department of Mathematics, The University of Auckland, Auckland, 2002.