title: Automatic simplification of systems of reaction-diffusion equations by a posteriori analysis.
abstract: Many mathematical models in biology and physiology are represented by systems of nonlinear differential equations. In recent years these models have become increasingly complex in order to explain the enormous volume of data now available. A key role of modellers is to determine which components of the model have the greatest effect on a given observed behaviour. An approach for automatically fulfilling this role, based on a posteriori analysis, has recently been developed for nonlinear initial value ordinary differential equations [J.P. Whiteley, Model reduction using a posteriori analysis, Math. Biosci. 225 (2010) 44-52]. In this paper we extend this model reduction technique for application to both steady-state and time-dependent nonlinear reaction-diffusion systems. Exemplar problems drawn from biology are used to demonstrate the applicability of the technique.
authors.affiliation: Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, United Kingdom. Electronic address: philip.maybank@gmail.com.
authors.forename: Philip J
authors.initials: PJ
authors.lastname: Maybank
authors.affiliation: Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, United Kingdom. Electronic address: jonathan.whiteley@cs.ox.ac.uk.
authors.forename: Jonathan P
authors.initials: JP
authors.lastname: Whiteley
mesh_terms: D000465:Algorithms; D004058:Diffusion; D007700:Kinetics; D016014:Linear Models; D055641:Mathematical Concepts; D008954:Models, Biological; D017711:Nonlinear Dynamics; D049490:Systems Biology
keywords: A posteriori; Model reduction; Reaction–diffusion