Order and effective order

Applied Numerical Mathematics

Volumn 28, Issue 2-4, 1998, Pages 179-191

  Butcher, J C ^a  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

Effective order; Runge Kutta methods

Indexed keywords

ALGEBRA; APPLICATIONS; ORDINARY DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

EFFECTIVE ORDER;

RUNGE KUTTA METHODS;

EID: 0032182452     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(98)00043-9     Document Type: Article

References (13)

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2. J.C. Butcher, The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods (Wiley, Chichester and New York, 1986).
3. J.C. Butcher and J.R. Cash, Towards efficient Runge-Kutta methods for stiff systems, SIAM J. Numer. Anal. 27 (1990) 753-761.
4. J.C. Butcher, J.R. Cash and M.T. Diamantakis, DESI methods for stiff initial value problems, ACM Trans. Math. Software 22 (1996) 401-422.
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6. J.C. Butcher and P. Chartier, The effective order of singly-implicit Runge-Kutta methods, under preparation.
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8. J.C. Butcher and J.M. Sanz-Serna, The number of conditions for a Runge-Kutta method to have effective order p, Appl. Numer. Math. 22 (1996) 103-111.
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10. A.R. Gifkins, An algebraic approach to Runge-Kutta methods, Ph.D. Thesis, University of Auckland (1972).
11. E. Hairer, S.P. Nørsett and G. Wanner, Solving Ordinary Differential Equations Numerically I: The Nonstiff Case (Springer, Berlin, 1993).
12. M.A. López-Marcos, J.M. Sanz-Serna and R.D. Skeel, Cheap enhancement of symplectic integrators, in: D.F. Griffiths and G.A. Watson, eds., Numerical Analysis 1995 (Longman, Harlow, 1996) 107-122.
13. H.J. Stetter, Local estimation of the global discretization error, SIAM J. Numer. Anal. 8 (1971) 512-523.