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Computing the moments of high dimensional solutions of the master equation
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis. (ndim)
2006 (English)In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 180, 498-515 p.Article in journal (Refereed) Published
Place, publisher, year, edition, pages
2006. Vol. 180, 498-515 p.
National Category
Computational Mathematics
URN: urn:nbn:se:uu:diva-84013DOI: 10.1016/j.amc.2005.12.032ISI: 000242276500008OAI: oai:DiVA.org:uu-84013DiVA: diva2:111921
Available from: 2006-11-11 Created: 2006-11-11 Last updated: 2011-11-29Bibliographically approved
In thesis
1. Numerical Solution Methods in Stochastic Chemical Kinetics
Open this publication in new window or tab >>Numerical Solution Methods in Stochastic Chemical Kinetics
2008 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This study is concerned with the numerical solution of certain stochastic models of chemical reactions. Such descriptions have been shown to be useful tools when studying biochemical processes inside living cells where classical deterministic rate equations fail to reproduce actual behavior. The main contribution of this thesis lies in its theoretical and practical investigation of different methods for obtaining numerical solutions to such descriptions.

In a preliminary study, a simple but often quite effective approach to the moment closure problem is examined. A more advanced program is then developed for obtaining a consistent representation of the high dimensional probability density of the solution. The proposed method gains efficiency by utilizing a rapidly converging representation of certain functions defined over the semi-infinite integer lattice.

Another contribution of this study, where the focus instead is on the spatially distributed case, is a suggestion for how to obtain a consistent stochastic reaction-diffusion model over an unstructured grid. Here it is also shown how to efficiently collect samples from the resulting model by making use of a hybrid method.

In a final study, a time-parallel stochastic simulation algorithm is suggested and analyzed. Efficiency is here achieved by moving parts of the solution phase into the deterministic regime given that a parallel architecture is available.

Necessary background material is developed in three chapters in this summary. An introductory chapter on an accessible level motivates the purpose of considering stochastic models in applied physics. In a second chapter the actual stochastic models considered are developed in a multi-faceted way. Finally, the current state-of-the-art in numerical solution methods is summarized and commented upon.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2008. 68 p.
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 564
stochastic models, chemical master equation, mesoscopic kinetics, Markov property, jump process, moment closure problem, spectral-Galerkin method, high dimensional problem, hybrid methods, time-parallel, homogenization
National Category
Computational Mathematics
Research subject
Scientific Computing with specialization in Numerical Analysis
urn:nbn:se:uu:diva-9342 (URN)978-91-554-7322-8 (ISBN)
Public defence
2008-11-28, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 13:15 (English)
Available from: 2008-11-07 Created: 2008-11-07 Last updated: 2011-10-26Bibliographically approved

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