A general theory of stabilized extended one-step methods for odes

International Journal of Computer Mathematics

Volumn 60, Issue 3-4, 1996, Pages 253-263

  Van Daele, M ^a   Vanden Berghe, G ^a   De Meyer, H ^a,b  

^a GHENT UNIVERSITY   (Belgium)

^b FUND FOR SCIENTIFIC RESEARCH   (Belgium)

Author keywords

A stability; Extended one step methods; Initial value problems; L stability; ODEs

Indexed keywords

COMPUTATIONAL METHODS; DIFFERENTIAL EQUATIONS; INTEGRATION; NUMERICAL METHODS;

A STABILITY; EXTENDED ONE STEP METHOD; INITIAL VALUE PROBLEMS; L STABILITY; LINEAR MULTISTEP METHODS; RUNGE KUTTA METHODS;

BOUNDARY VALUE PROBLEMS;

EID: 0029718139     PISSN: 00207160     EISSN: None     Source Type: Journal    
DOI: 10.1080/00207169608804490     Document Type: Article

References (10)

1. J. D. Lambert, Computational Methods in Ordinary Differential Equations (John Wiley, London, 1973).
2. R. S. Usmani, and R. P. Agarwal, An A-stable extended trapezoidal rule for the numerical integration of ordinary differential equations, Computers Math. Applic., 11 (1985) 1183-1191.
3. I. B. Jacques, Extended one-step methods for the numerical solution of ordinary differential equations, Intern. J. Computer Math., 29 (1989) 247-255.
4. M. M. Chawla, M. A. Al-Zanaidi, and M. S. Al-Sahhar, Stabilized fourth order extended methods for the numerical solution of ODEs, Intern. J. Computer Math., 52 (1994) 99-107.
5. M. M. Chawla, M. A. Al-Zanaidi, and M. S. Al-Sahhar, A class of stabilized extended one-step methods for the numerical solution of ODEs, Computers Math. Applic., 29 (1995) 79-84.
6. J. D. Lambert, Numerical Methods for Ordinary Differential Systems, The initial value problem (John Wiley & Sons, London. 1991).
7. J. C. Butcher, The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods (J. Wiley, Chichester), (1987).
8. A Iserles and S. P.Nørsett, Order stars (Chapman & Hall, London, 1991).
9. E. Hairer, and G. Wanner, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems (Springer-Verlag, Berlin, 1991).
10. W. Liniger and R. A. Willoughby, Efficient integration methods for stiff systems of ordinary differential equations, SIAM J. Numer. Anal., 7 (1970) 47-66.