Higher-order numerical methods for stochastic simulation of chemical reaction systems
In this paper, using the framework of extrapolation, we present an approach for obtaining higher-order -leap methods for the Monte Carlo simulation of stochastic chemical kinetics. Specifically, Richardson extrapolation is applied to the expectations of functionals obtained by a fixed-step -leap a...
| Main Authors: | , , , |
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| Format: | Journal article |
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2011
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| _version_ | 1797055999685689344 |
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| author | Székely Jr., T Burrage, K Erban, R Zygalakis, K |
| author_facet | Székely Jr., T Burrage, K Erban, R Zygalakis, K |
| author_sort | Székely Jr., T |
| collection | OXFORD |
| description | In this paper, using the framework of extrapolation, we present an approach for obtaining higher-order -leap methods for the Monte Carlo simulation of stochastic chemical kinetics. Specifically, Richardson extrapolation is applied to the expectations of functionals obtained by a fixed-step -leap algorithm. We prove that this procedure gives rise to second-order approximations for the first two moments obtained by the chemical master equation for zeroth- and first-order chemical systems. Numerical simulations verify that this is also the case for higher-order chemical systems of biological importance. This approach, as in the case of ordinary and stochastic differential equations, can be repeated to obtain even higher-order approximations. We illustrate the results of a second extrapolation on two systems. The biggest barrier for observing higher-order convergence is the Monte Carlo error; we discuss different strategies for reducing it. |
| first_indexed | 2024-03-06T19:17:19Z |
| format | Journal article |
| id | oxford-uuid:18dbec0b-f639-4e30-9829-3a0e278410ef |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:17:19Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:18dbec0b-f639-4e30-9829-3a0e278410ef2022-03-26T10:45:30ZHigher-order numerical methods for stochastic simulation of chemical reaction systemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:18dbec0b-f639-4e30-9829-3a0e278410efMathematical Institute - ePrints2011Székely Jr., TBurrage, KErban, RZygalakis, KIn this paper, using the framework of extrapolation, we present an approach for obtaining higher-order -leap methods for the Monte Carlo simulation of stochastic chemical kinetics. Specifically, Richardson extrapolation is applied to the expectations of functionals obtained by a fixed-step -leap algorithm. We prove that this procedure gives rise to second-order approximations for the first two moments obtained by the chemical master equation for zeroth- and first-order chemical systems. Numerical simulations verify that this is also the case for higher-order chemical systems of biological importance. This approach, as in the case of ordinary and stochastic differential equations, can be repeated to obtain even higher-order approximations. We illustrate the results of a second extrapolation on two systems. The biggest barrier for observing higher-order convergence is the Monte Carlo error; we discuss different strategies for reducing it. |
| spellingShingle | Székely Jr., T Burrage, K Erban, R Zygalakis, K Higher-order numerical methods for stochastic simulation of chemical reaction systems |
| title | Higher-order numerical methods for stochastic simulation of
chemical reaction systems |
| title_full | Higher-order numerical methods for stochastic simulation of
chemical reaction systems |
| title_fullStr | Higher-order numerical methods for stochastic simulation of
chemical reaction systems |
| title_full_unstemmed | Higher-order numerical methods for stochastic simulation of
chemical reaction systems |
| title_short | Higher-order numerical methods for stochastic simulation of
chemical reaction systems |
| title_sort | higher order numerical methods for stochastic simulation of chemical reaction systems |
| work_keys_str_mv | AT szekelyjrt higherordernumericalmethodsforstochasticsimulationofchemicalreactionsystems AT burragek higherordernumericalmethodsforstochasticsimulationofchemicalreactionsystems AT erbanr higherordernumericalmethodsforstochasticsimulationofchemicalreactionsystems AT zygalakisk higherordernumericalmethodsforstochasticsimulationofchemicalreactionsystems |