Type
ArticleAuthors
Whiteley, Jonathan P.KAUST Grant Number
KUK-C1-013-04Date
2010-05Permanent link to this record
http://hdl.handle.net/10754/598851
Metadata
Show full item recordAbstract
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 functional of interest. 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. © 2010 Elsevier Inc.Citation
Whiteley JP (2010) Model reduction using a posteriori analysis. Mathematical Biosciences 225: 44–52. Available: http://dx.doi.org/10.1016/j.mbs.2010.01.008.Sponsors
This publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).Publisher
Elsevier BVJournal
Mathematical BiosciencesPubMed ID
20117117ae974a485f413a2113503eed53cd6c53
10.1016/j.mbs.2010.01.008
Scopus Count
Collections
Publications Acknowledging KAUST SupportRelated articles
- A second-order algorithm for solving dynamic cell membrane equations.
- Authors: Sundnes J, Artebrant R, Skavhaug O, Tveito A
- Issue date: 2009 Oct
- Finite element methods for the biomechanics of soft hydrated tissues: nonlinear analysis and adaptive control of meshes.
- Authors: Spilker RL, de Almeida ES, Donzelli PS
- Issue date: 1992
- Automatic simplification of systems of reaction-diffusion equations by a posteriori analysis.
- Authors: Maybank PJ, Whiteley JP
- Issue date: 2014 Feb
- Model reduction for initial value ODEs.
- Authors: Ambuehl A, Whiteley JP
- Issue date: 2021 Jul
- Soft tissue modelling of cardiac fibres for use in coupled mechano-electric simulations.
- Authors: Whiteley JP, Bishop MJ, Gavaghan DJ
- Issue date: 2007 Oct