General linear methods

Computers and Mathematics with Applications

Volumn 31, Issue 4-5, 1996, Pages 105-112

  Butcher, J C ^a  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

Differential equations; General linear methods

Indexed keywords

EID: 23644439948     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/0898-1221(95)00222-7     Document Type: Article

References (11)

1. J.C. Butcher, On the convergence of numerical solutions to ordinary differential equations, Math. Comp. 20, 1-10 (1966).
2. C.W. Gear, Hybrid methods for inital value problems in ordinary differential equations, SIAM J. Numer. Anal. 2, 69-86 (1965).
3. W.B. Gragg and H.J. Stetter, Generalized multistep predictor-corrector methods, J. Assoc. Comput. Mach. 11, 188-209 (1964).
4. J.C. Butcher, A modified multistep method for the numerical integration of ordinary differential equations, J. Assoc. Comput. Mach. 12, 124-135 (1965).
5. J.C. Butcher, Diagonally implicit multi-stage integration methods, Appl. Numer. Math. 11, 347-363 (1993).
6. K. Burrage and J.C. Butcher, Non-linear stability of a general class of differential equation methods, BIT 20, 185-203 (1980).
7. J.C. Butcher, The effective order of Runge-Kutta methods, Lecture Notes in Mathematics 109, 133-139 (1969).
8. J.C. Butcher and Z. Jackiewicz, The construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations (in preparation).
9. J.C. Butcher and Z. Jackiewicz, Diagonally implicit general linear methods for ordinary differential equations, BIT 33, 452-472 (1993).
10. J.C. Butcher and Z. Jackiewicz, The implementation of diagonally implicit multistage integration methods for ordinary differential equations (in preparation).
11. J.C. Butcher and P. Chartier, Parallel general linear methods for stiff ordinary differential and differential algebraic equations, Appl. Numer. Math. 17, 213-222 (1995).