A Laplace transform approach to direct and inverse problems for multi-compartment models

Multi-compartment models described by systems of linear ordinary differential equations are considered. Catenary models are a particular class where the compartments are arranged in a chain. A unified methodology based on the Laplace transform is utilised to solve direct and inverse problems for mul...

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Bibliographic Details
Published inEuropean journal of applied mathematics Vol. 33; no. 6; pp. 1170 - 1184
Main Author RODRIGO, M.
Format Journal Article
LanguageEnglish
Published Cambridge Cambridge University Press 01.12.2022
Subjects
Applied mathematics
Catenaries
Differential equations
Inverse problems
Laplace transforms
Mathematical models
Parameter estimation
Polynomials
System theory
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ISSN0956-7925
1469-4425
DOI10.1017/S0956792522000055

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Summary:Multi-compartment models described by systems of linear ordinary differential equations are considered. Catenary models are a particular class where the compartments are arranged in a chain. A unified methodology based on the Laplace transform is utilised to solve direct and inverse problems for multi-compartment models. Explicit formulas for the parameters in a catenary model are obtained in terms of the roots of elementary symmetric polynomials. A method to estimate parameters for a general multi-compartment model is also provided. Results of numerical simulations are presented to illustrate the effectiveness of the approach.
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ISSN:0956-7925
1469-4425
DOI:10.1017/S0956792522000055