Numerical solution of stiff systems of differential equations arising from chemical reactions

Document Type : Research Article

Authors

1 Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.

2 Department of Mathematics, Faculty of Science, Malayer University, Malayer, Iran

Abstract

Long time integration of large stiff systems of initial value problems, arising from chemical reactions, demands efficient methods with good accuracy and extensive absolute stability region. In this paper, we apply second derivative general linear methods to solve some stiff chemical problems such as chemical Akzo Nobel problem, HIRES problem and OREGO problem.

Keywords


1.  Abdi, A. and Hojjati, G. An extension of general linear methods, Numer. Algor., 57 (2011), 149–167.
2. Abdi, A. and Hojjati, G. Maximal order for second derivative general linear methods with Runge-Kutta stability, Appl. Numer. Math., 61 (2011), 1046–1058.
3. Abdi, A., Bra` s, M. and Hojjati, G. On the construction of second derivative diagonally implicit multistage integration methods, Appl. Numer. Math., 76 (2014), 1–18.
4. Burg, K.V. Statistical Models in Applied Science, J. Wiley, New York, 1975.
5. Butcher, J. C. On the convergence of numerical solutions to ordinary differential equations, Math. Comp., 20 (1966), 1–10.
6. Butcher, J. C. and Hojjati, G. Second derivative methods with RK stability, Numer. Algor., 40 (2005), 415–429.
7. Cash, J. R. Second derivative extended backward differentiation formula for the numerical integration of stiff systems, SIAM J. Numer. Anal., 18 (1981), 21–36.
8. Enright, W. H. Second derivative multistep methods for stiff ordinary differential equations, SIAM J. Numer. Anal., 11 (1974), 321–331.
9. Hojjati, G., Rahimi Ardabili, M.Y. and Hosseini, S.M. New second derivative multistep methods for stiff systems, Appl. Math. Model., 30 (2006), 466–476.
10. Eriksson, K., Johnson, C. and Logg, A. Explicit time-stepping for stiff ODEs, SIAM J. Sci. Comput., 25 (2003), 11–42.
11. Field, R. J., K¨or¨os, E. and Noyes, R. M. Oscillation in chemical systems, part. 2. thorough analysis of temporal oscillations in the bromate–cerium–malonic acid system. Journal of the American Society, 94 (1972), 8649–8664.
12. Gray, C. An analysis of the Belousov–Zhabotinskii reaction. Rose-Hulman Undergraduate Mathematics Journal, 3(1), 2002. http://www.rose hulman.edu/mathjournal/.
13. Hairer, E. and Wanner, G. Solving Ordinary Differential Equations II: Stiff and Differential-algebraic Problems, Springer-Verlag, 1991.
14. Sch¨ afer, E. A new approach to explain the ‘high irradiance responses’ of photomorphogenesis on the bais of phytochrome, J. of Math. Biology, 2 (1975), 41–56.
CAPTCHA Image