On some aspects of casual and neutral equations used in mathematical modelling

Hdl Handle:
http://hdl.handle.net/10034/346437
Title:
On some aspects of casual and neutral equations used in mathematical modelling
Authors:
Baker, Christopher T. H.; Bocharov, Gennady; Parmuzin, Evgeny I.; Rihan, F. A. R.
Abstract:
The problem that motivates the considerations here is the construction of mathematical models of natural phenomena that depend upon past states. The paper divides naturally into two parts: in the first, we expound the inter-connection between ordinary differential equations, delay differential equations, neutral delay-differential equations and integral equations (with emphasis on certain linear cases). As we show, this leads to a natural hierarchy of model complexity when such equations are used in mathematical and computational modelling, and to the possibility of reformulating problems either to facilitate their numerical solution or to provide mathematical insight, or both. Volterra integral equations include as special cases the others we consider. In the second part, we develop some practical and theoretical consequences of results given in the first part. In particular, we consider various approaches to the definition of an adjoint, we establish (notably, in the context of sensitivity analysis for neutral delay-differential equations) roles for well-defined ad-joints and ‘quasi-adjoints’, and we explore relationships between sensitivity analysis, the variation of parameters formulae, the fundamental solution and adjoints.
Affiliation:
University of Chester
Citation:
Chester : University of Chester, 2007
Publisher:
University of Chester
Publication Date:
2007
URI:
http://hdl.handle.net/10034/346437
Additional Links:
http://www.chester.ac.uk
Type:
Technical Report
Language:
en
Series/Report no.:
Applied Mathematics Research Group Research Report; 2007 : 2
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorBaker, Christopher T. H.en
dc.contributor.authorBocharov, Gennadyen
dc.contributor.authorParmuzin, Evgeny I.en
dc.contributor.authorRihan, F. A. R.en
dc.date.accessioned2015-03-09T16:43:49Zen
dc.date.available2015-03-09T16:43:49Zen
dc.date.issued2007en
dc.identifier.citationChester : University of Chester, 2007en
dc.identifier.urihttp://hdl.handle.net/10034/346437en
dc.description.abstractThe problem that motivates the considerations here is the construction of mathematical models of natural phenomena that depend upon past states. The paper divides naturally into two parts: in the first, we expound the inter-connection between ordinary differential equations, delay differential equations, neutral delay-differential equations and integral equations (with emphasis on certain linear cases). As we show, this leads to a natural hierarchy of model complexity when such equations are used in mathematical and computational modelling, and to the possibility of reformulating problems either to facilitate their numerical solution or to provide mathematical insight, or both. Volterra integral equations include as special cases the others we consider. In the second part, we develop some practical and theoretical consequences of results given in the first part. In particular, we consider various approaches to the definition of an adjoint, we establish (notably, in the context of sensitivity analysis for neutral delay-differential equations) roles for well-defined ad-joints and ‘quasi-adjoints’, and we explore relationships between sensitivity analysis, the variation of parameters formulae, the fundamental solution and adjoints.en
dc.language.isoenen
dc.publisherUniversity of Chesteren
dc.relation.ispartofseriesApplied Mathematics Research Group Research Reporten
dc.relation.ispartofseries2007 : 2en
dc.relation.urlhttp://www.chester.ac.uken
dc.subjectcomputational modellingen
dc.subjectanalysis of modelsen
dc.subjectdelay & neutral-delay differential equationsen
dc.subjectVolterra integral equationsen
dc.subjectfundamental solutionsen
dc.subjectvariation of parametersen
dc.titleOn some aspects of casual and neutral equations used in mathematical modellingen
dc.typeTechnical Reporten
dc.contributor.departmentUniversity of Chesteren
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