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ABSOLUTELY STABLE EXPLICIT SCHEMES FOR REACTION SYSTEMS
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 Title & Authors
ABSOLUTELY STABLE EXPLICIT SCHEMES FOR REACTION SYSTEMS
Lee, Chang-Ock; Leem, Chae-Hun; Park, Eun-Hee; Youm, Jae-Boum;
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 Abstract
We introduce two numerical schemes for solving a system of ordinary differential equations which characterizes several kinds of linear reactions and diffusion from biochemistry, physiology, etc. The methods consist of sequential applications of the simple exact solver for a reversible reaction. We prove absolute stability and convergence of the proposed explicit methods. One is of first order and the other is of second order. Numerical results are included.
 Keywords
reaction system;chemical diffusion;absolutely stable scheme;explicit scheme;
 Language
English
 Cited by
1.
Analysis of factors affecting Ca2+-dependent inactivation dynamics of L-type Ca2+current of cardiac myocytes in pulmonary vein of rabbit, The Journal of Physiology, 2012, 590, 18, 4447  crossref(new windwow)
 References
1.
J. C. Butcher and H. Podhaisky, On error estimation in general linear methods for stiff ODEs, Appl. Numer. Math. 56 (2006), no. 3-4, 345-357 crossref(new window)

2.
K. Eriksson, C. Johnson, and A. Logg, Explicit time-stepping for stiff ODEs, SIAM J. Sci. Comput. 25 (2003/04), no. 4, 1142-1157 crossref(new window)

3.
E. Hairer and G. Wanner, Solving Ordinary Differential Equations. II, Springer Series in Computational Mathematics, 14. Springer-Verlag, Berlin, 1991

4.
M. Inc, New L-stable method for numerical solutions of ordinary differential equations, Appl. Math. Comput. 188 (2007), no. 1, 779-785 crossref(new window)

5.
A. Iserles, Composite methods for numerical solution of stiff systems of ODEs, SIAM J. Numer. Anal. 21 (1984), no. 2, 340-351 crossref(new window)

6.
J. Keener and J. Sneyd, Mathematical Physiology, Interdisciplinary Applied Mathematics, 8. Springer-Verlag, New York, 1998

7.
M. W. J. M. Musters, J. B. Basssingthwaighte, V. Panday, N. A. W. van Riel, and G. J. van der Vusse, Computational modeling of cardiac fatty acid uptake and utilization, 173-224, G. J. van den Vusse, Amsterdam, Lipobiology, Elsevier, 2004

8.
N. C. Price and R. A. Dwek, Principles and Problems in Physical Chemistry for Biochemists, Oxford University Press, Oxford, 1979

9.
S. Rush and H. Larsen, A practical algorithm for solving dynamic membrane equations, IEEE Trans. Biomed. Eng. 25 (1978), 389-392 crossref(new window)

10.
W. Simon, Mathematical Techniques for Biology and Medicine, Third edition. Dover Publications, Inc., New York, 1986

11.
M. Tokman, Efficient integration of large stiff systems of ODEs with exponential propagation iterative (EPI) methods, J. Comput. Phys. 213 (2006), no. 2, 748-776 crossref(new window)

12.
W.Walter, Ordinary Differential Equations, Graduate Texts in Mathematics, 182. Readings in Mathematics. Springer-Verlag, New York, 1998