Spatially distributed stochastic systems: Equation-free and equation-assisted preconditioned computations

Journal of Chemical Physics

Volumn 125, Issue 20, 2006, Pages

  Qiao, Liang ^a   Erban, Radek ^b   Kelley, C T ^c   Kevrekidis, Ioannis G ^a,d  

^a Princeton University   (United States)

^b UNIVERSITY OF OXFORD   (United Kingdom)

^c NORTH CAROLINA STATE UNIVERSITY   (United States)

^d PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COARSE-GRAINED QUANTITIES; REACTION-DIFFUSION MODEL; SPATIALLY DISTRIBUTED STOCHASTIC SYSTEMS; STOCHASTIC COMPUTATIONS;

COMPUTATION THEORY; DIFFUSION; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

STOCHASTIC CONTROL SYSTEMS;

ALGORITHM; ARTICLE; CHEMICAL MODEL; CHEMICAL STRUCTURE; COMPUTER SIMULATION; DIFFUSION; STATISTICAL MODEL; STATISTICS;

ALGORITHMS; COMPUTER SIMULATION; DIFFUSION; MODELS, CHEMICAL; MODELS, MOLECULAR; MODELS, STATISTICAL; STOCHASTIC PROCESSES;

EID: 33751561755     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2372492     Document Type: Article

References (37)

1. H. S. Fogler, Elements of Chemical Reaction Engineering (Prentice-Hall, Englewood Cliffs, NJ, 2005).
2. J. D. Murray, Mathematical Biology (Springer, Berlin, 2002).
3. I. G. Kevrekidis, C. W. Gear, J. M. Hyman, P. G. Kevrekidis, O. Runborg, and C. Theodoropoulos, Commun. Math. Sci. 1, 175 (2003).
4. C. W. Gear, I. G. Kevrekidis, and C. Theodoropoulos, Comput. Chem. Eng. 26, 941 (2002).
5. O. Runborg, C. Theodoropoulos, and I. G. Kevrekidis, Nonlinearity 15, 491 (2002).
6. A. G. Makeev, D. Maroudas, A. Z. Panagiotopoulos, and I. G. Kevrekidis, J. Chem. Phys. 117, 8229 (2002).
7. R. Erban, I. G. Kevrekidis, D. Adalsteinsson, and T. C. Elston, J. Chem. Phys. 124, 084106 (2006).
8. H. Salis and Y. N. Kaznessis, J. Chem. Phys. 123, 214106 (2005).
9. C. R. Laing, J. Comput. Neurosci. 20, 5 (2006).
10. G. Samaey, W. Vanroose, D. Roose, and I. G. Kevrekidis, J. Comput. Phys. (to be published).
11. C. Cercignani, The Boltzmann Equation and Its Applications, Applied Mathematical Sciences, Vol. 67 (Springer-Verlag, Berlin, 1988).
12. R. Erban and H. G. Othmer, SIAM J. Appl. Math. 65, 361 (2004).
13. R. Erban and H. G. Othmer, J. Math. Biol. (to be published).
14. A. M. Turing, Philos. Trans. R. Soc. London, Ser. B 237, 37 (1952).
15. O. Shimmi, D. Umulis, H. Othmer, and M. B. O'Connor, Cell 120, 873 (2005).
16. G. T. Reeves, R. Kalifa, D. E. Klein, M. A. Lemmon, and S. Y. Shvartsmann, Dev. Biol. 284, 523 (2005).
17. J. Schnakenberg, J. Theor. Biol. 81, 389 (1979).
18. J. A. Izaguirre, R. Chaturvedi, C. Huang, Bioinformatics 20, 1129 (2004).
19. D. T. Gillespie, J. Phys. Chem. 81, 2340 (1977).
20. A. B. Stundzia and C. J. Lumsden, J. Comput. Phys. 127, 196 (1996).
21. S. A. Isaacson and C. S. Peskin, SIAM J. Sci. Comput. (USA) 28, 47 (2006).
22. E. J. Doedel, Congr. Numer. 30, 265 (1981).
23. Y. A. Kuznetsov and V. V. Levitin, CONTENT, a multiplatform environment for analyzing dynamical systems, Dynamical Systems Laboratory, CWI, Amsterdam, 1995-1997.
24. G. M. Shroff and H. B. Keller, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 30, 1099 (1993).
25. L. S. Tuckerman and D. Barkley, Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems, IMA Volumes in Mathematics and its Applications, Vol. 119 (Springer, New York, 1999), pp. 453-466.
26. C. T. Kelley, Iterative Methods for Linear and Nonlinear Equations, Frontiers in Applied Mathematics, Vol. 16 (SIAM, Philadelphia, 1995).
27. C. Theodoropoulos, Y.-H. Qian, and I. G. Kevrekidis, Proc. Natl. Acad. Sci. U.S.A. 97, 9840 (2000).
28. C. T. Kelley, Solving Nonlinear Equations with Newton's Method, Fundamental Algorithms for Numerical Calculations, Vol. 1 (SIAM, Philadelphia, 2003).
29. V. Simoncini and D. B. Szyld, SIAM J. Sci. Comput. (USA) 25, 454 (2003).
30. J. van den Eshof and G. L. G. Sleijpen, SIAM J. Matrix Anal. Appl. 26, 125 (2004).
31. A. Bouras and V. Fraysś, SIAM J. Matrix Anal. Appl. 26, 660 (2005).
32. C. V. Rao and A. P. Arkin, J. Chem. Phys. 118, 4999 (2003).
33. E. L. Haseltine and J. B. Rawlings, J. Chem. Phys. 117, 6959 (2002).
34. Y. Cao, D. T. Gillespie, and L. R. Petzold, J. Chem. Phys. 122, 014116 (2005).
35. M. A. Katsoulakis, A. J. Majda, and D. G. Vlachos, Proc. Natl. Acad. Sci. U.S.A. 100, 782 (2003).
36. M. A. Katsoulakis, A. J. Majda, and D. G. Vlachos, J. Comput. Phys. 186, 250 (2003).
37. I. G. Kevrekidis, B. Nicolaenko, and J. C. Scovel, SIAM J. Appl. Math. 50, 760 (1990).