Stability regions of one step mixed collocation methods for y″ = f(x,y)

Applied Numerical Mathematics

Volumn 53, Issue 2-4, 2005, Pages 201-212

  Carpentieri, M ^a   Paternoster, B ^a  

^a UNIVERSITY OF SALERNO   (Italy)

Author keywords

Collocation methods; Numerical methods for ODEs; Runge Kutta Nystr m methods; Stability analysis

Indexed keywords

ALGEBRA; HARMONIC ANALYSIS; INITIAL VALUE PROBLEMS; INTEGRATION; NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS; OSCILLATIONS; POLYNOMIALS;

COLLOCATION METHODS; NUMERICAL METHODS FOR ODES; RUNGE-KUTTA-NYSTRÖM METHODS; STABILITY ANALYSIS;

RUNGE KUTTA METHODS;

EID: 14844290293     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2004.08.020     Document Type: Conference Paper

References (15)

1. M. Cafaro, and B. Paternoster Analysis of stability of rational approximations through computer algebra V.G. Ganzha E.W. Mayr E.V. Vorozhtsov Computer Algebra in Scientific Computing CASC-99, Munich, 1999 1999 Springer Berlin 25 36
2. M. Carpentieri, B. Paternoster, Stability analysis of frequency and step length dependent Runge-Kutta-Nyström methods, Future Generat. Comput. Systems, in press
3. J.P. Coleman, and L.Gr. Ixaru P-stability and exponential-fitting methods for y″ = f (x,y) IMA J. Numer. Anal. 16 1996 179 199
4. J.P. Coleman, and S.C. Duxbury Mixed collocation methods for y″ = f (x,y) J. Comput. Appl. Math. 126 2000 47 75
5. K. Dekker, and J.G. Verwer Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations CWI Monograph 1984 North-Holland Amsterdam
6. E. Hairer, S.P. Norsett, and G. Wanner Solving Ordinary Differential Equations I - Nonstiff Problems Springer Series in Computational Mathematics vol. 8 1987 Springer Berlin
7. L.Gr. Ixaru, and B. Paternoster A conditionally P-stable fourth-order exponential-fitting method for y″ = f (x,y) J. Comput. Appl. Math. 106 1999 87 98
8. L. Kramarz Stability of collocation methods for the numerical solution of y″ = f (x,y) BIT 20 1980 215 222
9. J.D. Lambert Numerical Methods for Ordinary Differential Systems; The Initial Value Problem 1991 Wiley New York
10. B. Paternoster Runge-Kutta(-Nyström) methods for ODEs with periodic solutions based on trigonometric polynomials Appl. Numer. Math. 28 2-4 1998 401 412
11. B. Paternoster A phase-fitted collocation-based Runge-Kutta-Nyström method Appl. Numer. Math. 35 4 2000 239 355
12. B. Paternoster, and M. Cafaro Computation of the interval of stability of Runge-Kutta-Nyström methods J. Symbolic Comput. 25 3 1998 383 394
13. L.R. Petzold, L.O. Jay, and J. Yen Numerical solution of highly oscillatory ordinary differential equations Acta Numerica 1997 Cambridge University Press Cambridge 437 483
14. P.J. van der Houwen, and B.P. Sommeijer Diagonally implicit Runge-Kutta-Nyström methods for oscillatory problems SIAM J. Numer. Anal. 26 1989 414 429
15. P.J. van der Houwen, B.P. Sommeijer, and N.H. Cong Stability of collocation-based Runge-Kutta-Nyström methods BIT 31 1991 469 481