References
- T.H. Ahn and A. Sandu. Implicit simulation methods for stochastic chemical kinetics, 2013. http://arxiv.org/abs/1303.3614
- T.H. Ahn, A. Sandu, L. Watson, C. Shaffer, Y. Cao and W. Baumann. Parallel load balancing strategies for ensembles of stochastic biochemical simulations. Tech. rep., Virginia Tech., 2012.
- Y. Cao, D.T. Gillespie and L.R. Petzold. The slow-scale stochastic simulation algorithm. J. Chemical Physics, 122:014116, 2005. http://dx.doi.org/10.1063/1.1824902.
- Y. Cao, H. Li and L. Petzold. Efficient formulation of the stochastic simulation algorithm for chemically reacting systems. J. Chemical Physics, 9(121):4059–4067, 2004. http://dx.doi.org/10.1063/1.1778376.
- Y. Cao, R. Petzold, M. Rathinam and D. Gillespie. The numerical stability of leaping methods for stochastic simulation of chemically reacting systems. J. Chemical Physics, 121(24):12169–12178, 2004. http://dx.doi.org/10.1063/1.1823412.
- S. Engblom. Numerical methods for the chemical master equation. Ph.D. thesis, Uppsala University, Department of Information Technology, 2006.
- D. Gillespie and L. Petzold. Improved leap-size selection for accelerated stochas- tic simulation. J. Chemical Physics, 119(16):8229–8234, 2003. http://dx.doi.org/10.1063/1.1613254.
- D.T. Gillespie. Exact stochastic simulation of coupled chemical reactions. J. Chemical Physics, 81(25):2340–2361, 1977. http://dx.doi.org/10.1021/j100540a008.
- D.T. Gillespie. Approximate accelerated stochastic simulation of chemically reacting systems. J. Chemical Physics, 115(4):1716–1733, 2001. http://dx.doi.org/10.1063/1.1378322.
- T. Kurtz. The relationship between stochastic and deterministic models for chemical reactions. J. Chemical Physics, 57(7):2976–2978, 1972. http://dx.doi.org/10.1063/1.1678692.
- S. MacNamara, K. Burrage and R.B. Sidje. Multiscale modeling of chemical kinetics via the master equation. SIAM J. Multiscale Modeling and Simulation, 4(6):1146–1168, 2008. http://dx.doi.org/10.1137/060678154.
- M. Rathinam, L. Petzold, Y. Cao and D. Gillespie. Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method. J. Chemical Physics, 119(24):12784, 2003. http://dx.doi.org/10.1063/1.1627296.
- M. Rathinam, L. Petzold, Y. Cao and D. Gillespie. Consistency and stability of tau leaping schemes for chemical reaction systems. SIAM J. Multiscale Modeling and Simulation, 3(4):867–895, 2005. http://dx.doi.org/10.1137/040603206.
- A. Sandu. A new look at chemical master equation. Numer. Algorithms, 65(3):485–498, 2013. http://dx.doi.org/10.1007/s11075-013-9758-z.
- G. Strang. On the construction and comparison of difference schemes. SIAM J. Numer. Anal., 3(5):506–517, 1968. http://dx.doi.org/10.1137/0705041.