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Lee, Chang Hyeong
Stochastic Analysis & Simulation(SAS) Lab
Research Interests
  • Stochastic analysis/computation, epidemic modeling, biological system simulation

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Perturbation and Truncation of Probability Generating Function Methods for Stiff Chemical Reactions

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Title
Perturbation and Truncation of Probability Generating Function Methods for Stiff Chemical Reactions
Author
Jeong, SoyeongKim, PilwonLee, Chang Hyeong
Issue Date
2015-02
Publisher
HINDAWI PUBLISHING CORPORATION
Citation
JOURNAL OF APPLIED MATHEMATICS, v.2015, pp.864238
Abstract
One can reformulate chemical master equations of the stochastic reaction network into a partial differential equation (PDE) of a probability generating function (PGF). In this paper, we present two improvements in such PGF-PDE approach, based on perturbation and double-truncation, respectively. The stiff system that involves fast and slow reactions together often requires high computational cost. By applying the perturbation method to PGF-PDEs, we expand the equation in terms of a small reaction rate which is often responsible for such stiffness of the system. Also by doubly truncating, we dump relatively small terms and reduce the computational load significantly at each time step. The terms corresponding to rare events are sieved out through truncations of Taylor expansion. It is shown through numerical examples of enzyme kinetics, transition model, and Brusselator model that the suggested method is accurate and efficient for approximation of the state probabilities. © 2015 Soyeong Jeong et al.
URI
https://scholarworks.unist.ac.kr/handle/201301/13391
URL
http://www.hindawi.com/journals/jam/2015/864238/
DOI
10.1155/2015/864238
ISSN
1110-757X
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