Implementation of diagonally implicit multistage integration methods for ordinary differential equations

SIAM Journal on Numerical Analysis

Volumn 34, Issue 6, 1997, Pages 2119-2141

  Butcher, J C ^a   Jackiewicz, Z ^b  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

^b ARIZONA STATE UNIVERSITY   (United States)

Author keywords

Continuous interpolants; General linear method; Local error estimation; Nordsieck technique

Indexed keywords

EID: 0000452884     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142995282509     Document Type: Article

References (10)

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4. J. C. BUTCHER AND Z. JACKIEWICZ, Diagonally implicit general linear methods for ordinary differential equations, BIT, 33 (1993), pp. 452-472.
5. 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), pp. 385-415.
6. E. HAIRER, S. P. NØRSETT, AND G. WANNER, Solving Ordinary Differential Equations I. Nonstiff Problems, Springer-Verlag, Berlin, Heidelberg, New York, 1993.
7. Z. JACKIEWICZ, R. VERMIGLIO, AND M. ZENNARO, Variable stepsize diagonally implicit multistage integration methods for ordinary differential equations, Appl. Numer. Math., 16 (1995), pp. 343-367.
8. Z. JACKIEWICZ, R. VERMIGLIO, AND M. ZENNARO, Regularity properties of multistage integration methods, J. Comp. Appl. Math., submitted.
9. A. NORDSIECK, On numerical integration of ordinary differential equations, Math. Comp., 16 (1962), pp. 22-49.
10. 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 (1974), pp. 145-162.