Adaptive time-stepping using control theory for the chemical Langevin equation
type: Item
instance of: scholarly article
title: Adaptive time-stepping using control theory for the chemical Langevin equation
zbMATH Open document ID: 1347.92024
DOI: 10.1155/2015/567275
author: Silvana Ilie
author: Monjur Morshed
published in: Journal of Applied Mathematics
publication date: 2016-10-19T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 92C40
Mathematics Subject Classification ID: 93E03
zbMATH DE Number: 6640991
zbMATH Keywords: Langevin equation
zbMATH Keywords: noncommutative noise
zbMATH Keywords: Milstein scheme
describes a project that uses: Hy3S
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/567275
OpenAlex ID: W2083992072
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Wikidata QID: Q59111896
DBLP publication ID: journals/jam/IlieM15
description: scientific article; zbMATH DE number 6640991