A second-order scheme for the "Brusselator" reaction-diffusion system

Journal of Mathematical Chemistry

Volumn 26, Issue 4, 1999, Pages 297-316

  Twizell, E H ^a   Gumel, A B ^b   Cao, Q ^c  

^a BRUNEL UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF MANITOBA   (Canada)

^c SHANDONG UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033114412     PISSN: 02599791     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1019158500612     Document Type: Article

References (13)

1. G. Adomian, The diffusion Brusselator equation, Comput. Math. Appl. 29(5) (1995) 1.
2. R.L. Burden and J.D. Faires, Numerical Analysis (Brooks/Cole, Pacific Grove, CA, 1997) (6th edition).
3. Y.S. Chen and A.Y.T. Leung, Bifurcations and Chaos in Engineering (Springer-Verlag, Berlin, 1998).
4. J. Gukenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcation of Vector Fields (Springer-Verlag, Berlin, 1983).
5. M. Herschkowitz-Kaufman and G. Nicolis, Localized spatial structures and non-linear chemical waves in dissipative systems, J. Chem. Phys. 56 (1972) 1890.
6. B. Lavenda, G. Nicolis and M. Herschkowitz-Kaufman, Chemical instabilities and relaxation oscillations, J. Theor. Biol. 32 (1971) 283.
7. R. Lefever, Dissipative structures in chemical systems, J. Chem. Phys. 49(11) (1968) 4977.
8. R. Lefever and G. Nicolis, Chemical instabilities and sustained oscillations, J. Theor. Biol. 30 (1971) 267.
9. G. Nicolis and I. Prigogine, Self-organization in Non-equilibrium Systems (Wiley Interscience, New York, 1977).
10. I. Prigogine and R. Lefever, Symmetry breaking instabilities in dissipative systems II, J. Chem. Phys. 48 (1968) 1695.
11. A.M. Turing, The chemical basis of morphogenesis, Philos. Trans. Roy. Soc. London Ser. B 237 (1952) 37.
12. E.H. Twizell, Yigong Wang and W.G. Price, Chaos-free numerical solutions of reaction-diffusion equations, Proc. Roy. Soc. London Ser. A 430 (1990) 541.
13. J. Tyson, Some further studies of non-linear oscillations in chemical systems, J. Chem. Phys. 58 (1973) 3919.