Whiteley, J. P. (2009) Model reduction using a posteriori analysis. Not specified . (Submitted)

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Abstract
Mathematical models in biology and physiology are often represented by large systems of non–linear ordinary differential equations. In many cases, an observed behaviour may be written as a linear functional of the solution of this system of equations. A technique is presented in this study for automatically identifying key terms in the system of equations that are responsible for a given linear functional of the solution. This technique is underpinned by ideas drawn from a posteriori error analysis. This concept has been used in finite element analysis to identify regions of the computational domain and components of the solution where a fine computational mesh should be used to ensure accuracy of the numerical solution. We use this concept to identify regions of the computational domain and components of the solution where accurate representation of the mathematical model is required for accuracy of the solution. The technique presented is demonstrated by application to a model problem, and then to automatically deduce known results from a cell–level cardiac electrophysiology model.
Item Type:  Article 

Subjects:  H  N > Numerical analysis 
Research Groups:  Oxford Centre for Collaborative Applied Mathematics 
ID Code:  811 
Deposited By:  Dr M. Stoll 
Deposited On:  23 Sep 2009 07:28 
Last Modified:  29 May 2015 18:30 
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