Order and stability of generalized Padé approximations

Applied Numerical Mathematics

Volumn 59, Issue 3-4, 2009, Pages 558-567

  Butcher, J C ^a  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

Generalized Pad approximations; Order; Order arrows; Order barriers; Order stars; Pad approximations; Stability

Indexed keywords

FUNCTIONS; POLYNOMIAL APPROXIMATION; STARS;

EXPONENTIAL FUNCTIONS; ORDER; ORDER ARROWS; ORDER BARRIERS; ORDER STARS; STABILITY POLYNOMIALS; STABILITY THEOREMS; STABLE METHODS;

CONVERGENCE OF NUMERICAL METHODS;

EID: 58249086598     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2008.03.006     Document Type: Article

References (7)

1. Butcher J.C. The A-stability of methods with Padé and generalized Padé stability functions. Numer. Algorithms 31 (2002) 47-58
2. Butcher J.C. General linear methods. Acta Numer. 15 (2006) 157-258
3. Butcher J.C. Numerical Methods for Ordinary Differential Equations. second ed. (2008), Wiley, Chichester, New York
4. Butcher J.C., and Chipman F.H. Generalized Padé approximations to the exponential function. BIT 32 (1992) 118-130
5. Ehle B.L. A-stable methods and Padé approximations to the exponential. SIAM J. Math. Anal. 4 (1973) 671-680
6. Iserles A., and Nørsett S.P. Order Stars (1991), Chapman and Hall, London
7. Wanner G., Hairer E., and Nørsett S.P. Order stars and stability theorems. BIT 18 (1978) 475-489