Adaptive Time-Stepping Using Control Theory for the Chemical Langevin Equation
Stochastic modeling of biochemical systems has been the subject of intense research in recent years due to the large number of important applications of these systems. A critical stochastic model of well-stirred biochemical systems in the regime of relatively large molecular numbers, far from the th...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2015/567275 |
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| author | Silvana Ilie Monjur Morshed |
| author_facet | Silvana Ilie Monjur Morshed |
| author_sort | Silvana Ilie |
| collection | DOAJ |
| description | Stochastic modeling of biochemical systems has been the subject of intense research in recent years due to the large
number of important applications of these systems. A critical stochastic model of well-stirred biochemical systems in
the regime of relatively large molecular numbers, far from the thermodynamic limit, is the chemical Langevin equation.
This model is represented as a system of stochastic differential equations, with multiplicative and noncommutative
noise. Often biochemical systems in applications evolve on multiple time-scales; examples include slow transcription
and fast dimerization reactions. The existence of multiple time-scales leads to mathematical stiffness, which is a major
challenge for the numerical simulation. Consequently, there is a demand for efficient and accurate numerical methods to
approximate the solution of these models. In this paper, we design an adaptive time-stepping method, based on control
theory, for the numerical solution of the chemical Langevin equation. The underlying approximation method is the
Milstein scheme. The adaptive strategy is tested on several models of interest and is shown to have improved efficiency
and accuracy compared with the existing variable and constant-step methods. |
| format | Article |
| id | doaj-art-577f2214d0f94991b3ba3ce00a0ebfb1 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-577f2214d0f94991b3ba3ce00a0ebfb12025-02-03T05:48:29ZengWileyJournal of Applied Mathematics1110-757X1687-00422015-01-01201510.1155/2015/567275567275Adaptive Time-Stepping Using Control Theory for the Chemical Langevin EquationSilvana Ilie0Monjur Morshed1Department of Mathematics, Ryerson University, Toronto, ON, M5B 2K3, CanadaDepartment of Applied Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, CanadaStochastic modeling of biochemical systems has been the subject of intense research in recent years due to the large number of important applications of these systems. A critical stochastic model of well-stirred biochemical systems in the regime of relatively large molecular numbers, far from the thermodynamic limit, is the chemical Langevin equation. This model is represented as a system of stochastic differential equations, with multiplicative and noncommutative noise. Often biochemical systems in applications evolve on multiple time-scales; examples include slow transcription and fast dimerization reactions. The existence of multiple time-scales leads to mathematical stiffness, which is a major challenge for the numerical simulation. Consequently, there is a demand for efficient and accurate numerical methods to approximate the solution of these models. In this paper, we design an adaptive time-stepping method, based on control theory, for the numerical solution of the chemical Langevin equation. The underlying approximation method is the Milstein scheme. The adaptive strategy is tested on several models of interest and is shown to have improved efficiency and accuracy compared with the existing variable and constant-step methods.http://dx.doi.org/10.1155/2015/567275 |
| spellingShingle | Silvana Ilie Monjur Morshed Adaptive Time-Stepping Using Control Theory for the Chemical Langevin Equation Journal of Applied Mathematics |
| title | Adaptive Time-Stepping Using Control Theory for the Chemical Langevin Equation |
| title_full | Adaptive Time-Stepping Using Control Theory for the Chemical Langevin Equation |
| title_fullStr | Adaptive Time-Stepping Using Control Theory for the Chemical Langevin Equation |
| title_full_unstemmed | Adaptive Time-Stepping Using Control Theory for the Chemical Langevin Equation |
| title_short | Adaptive Time-Stepping Using Control Theory for the Chemical Langevin Equation |
| title_sort | adaptive time stepping using control theory for the chemical langevin equation |
| url | http://dx.doi.org/10.1155/2015/567275 |
| work_keys_str_mv | AT silvanailie adaptivetimesteppingusingcontroltheoryforthechemicallangevinequation AT monjurmorshed adaptivetimesteppingusingcontroltheoryforthechemicallangevinequation |