A variable-step variable-order algorithm for systems of stiff ODEs

International Journal of Computer Mathematics

Volumn 63, Issue 1-2, 1997, Pages 149-157

  Van Hecke, T ^a   Vanden Berghe, G ^a   Van Daele, M ^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; Numerical algorithms; ODEs

Indexed keywords

COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

INITIAL VALUE PROBLEMS; ORDINARY DIFFERENTIAL EQUATIONS; RUNGE-KUTTA METHODS;

ALGORITHMS;

EID: 0030787689     PISSN: 00207160     EISSN: None     Source Type: Journal    
DOI: 10.1080/00207169708804557     Document Type: Article

References (14)

1. Van Daele, M., Vanden Berghe, G. and De Meyer, H. (1996). A general theory of stabilized extended one-step methods for ODEs, Intern. J. Computer Math., 60, 253-263.
2. Usmani, R-S. and Agarwal, R. P. (1985). An A-stable extended trapezoidal rule for the numerical integration of ordinary differential equations, Computers Math. Applic., 11, 1183-1191.
3. Jacques, I. B. (1989). Extended one-step methods for the numerical solution of ordinary differential equations, Intern. J. Computer Math, 29, 247-255.
4. Chawla, M. M., Al-Zanaidi, M. A. and Al-Sahhar, M. S. (1994) Stabilized fourth order extended methods for the numerical solution of ODEs, Intern. J. Computer Math., 52, 99-107.
5. Chawla, M. M., Al-Zanaidi, M. A. and Al-Sahhar, M. S. (1995). A class of stabilized extended one-step methods for the numerical solution of ODEs, Computers Math. Applic., 29, 79-84.
6. Cash, J. R. and Singhal, A. (1982). Mono-implicit Runge-Kutta formulae for the numerical integration of stiff differential equations, IMA J. Num. Anal., 2, 211-227.
7. Van Bokhoven, W. M. G. (1980). Efficient higher order implicit one-step methods for the integration of stiff differential equations, BIT, 20, 34-43.
8. Brown, P. N., Hindmarsh, A. C. and Byrne, G. D. (August 1992). VODE: A variable coefficient ODE solver, available via WWW at URL http://www.netlib.org/ode/vode.f.
9. van der Houwen, P. J., Hoffmann, W., Sommeijer, B. P., Lioen, W. M., van der Veen, W. A., de Swart, J. J. B. Test Set for IVP Solvers, CWI publication, also available via WWW page at URL http://www.cwi.nl/cwi/projects/IVPtestset.html.
10. Hairer, E. and Wanner, G. (1991). Solving Ordinary Differential Equations II: Stiff and Differential-algebraic Problems. Springer-Verlag.
11. The NAG Fortran Library Manual, (Mark 14) (1990) NAG Ltd. Oxford.
12. Schäfer, E. (1975). A new approach to explain the high irradiance responses of photomorphogenesis on the basis of phytochrome, J. of Math. Biology., 2, 41-56.
13. Verwer, J. G. (1994). Gauss-Seidel iteration for stiff ODEs from chemical kinetics, SIAM J. Sci. Comptit., 15, 1243-1259
14. Dormand, J. R. and Prince, P. J. (1980). A family of embedded Runge-Kutta formulae, J. Comp. and Appl. Math., 6, 19-26.