The numerical solution of fractional and distributed order differential equations

Hdl Handle:
http://hdl.handle.net/10034/76687
Title:
The numerical solution of fractional and distributed order differential equations
Authors:
Connolly, Joseph A.
Abstract:
Fractional Calculus can be thought of as a generalisation of conventional calculus in the sense that it extends the concept of a derivative (integral) to include non-integer orders. Effective mathematical modelling using Fractional Differential Equations (FDEs) requires the development of reliable flexible numerical methods. The thesis begins by reviewing a selection of numerical methods for the solution of Single-term and Multi-term FDEs. We then present: 1. a graphical technique for comparing the efficiency of numerical methods. We use this to compare Single-term and Multi-term methods and give recommendations for which method is best for any given FDE. 2. a new method for the solution of a non-linear Multi-term Fractional Dif¬ferential Equation. 3. a sequence of methods for the numerical solution of a Distributed Order Differential Equation. 4. a discussion of the problems associated with producing a computer program for obtaining the optimum numerical method for any given FDE.
Advisors:
Ford, Neville J.; Edwards, John T.
Publisher:
University of Liverpool (University College Chester)
Publication Date:
Dec-2004
URI:
http://hdl.handle.net/10034/76687
Type:
Thesis or dissertation
Language:
en
Sponsors:
Funded by a Chester College bursary
Appears in Collections:
Theses

Full metadata record

DC FieldValue Language
dc.contributor.advisorFord, Neville J.en
dc.contributor.advisorEdwards, John T.en
dc.contributor.authorConnolly, Joseph A.en
dc.date.accessioned2009-08-07T13:57:33Zen
dc.date.available2009-08-07T13:57:33Zen
dc.date.issued2004-12en
dc.identifieruk.bl.ethos.420746en
dc.identifier.urihttp://hdl.handle.net/10034/76687en
dc.description.abstractFractional Calculus can be thought of as a generalisation of conventional calculus in the sense that it extends the concept of a derivative (integral) to include non-integer orders. Effective mathematical modelling using Fractional Differential Equations (FDEs) requires the development of reliable flexible numerical methods. The thesis begins by reviewing a selection of numerical methods for the solution of Single-term and Multi-term FDEs. We then present: 1. a graphical technique for comparing the efficiency of numerical methods. We use this to compare Single-term and Multi-term methods and give recommendations for which method is best for any given FDE. 2. a new method for the solution of a non-linear Multi-term Fractional Dif¬ferential Equation. 3. a sequence of methods for the numerical solution of a Distributed Order Differential Equation. 4. a discussion of the problems associated with producing a computer program for obtaining the optimum numerical method for any given FDE.en
dc.description.sponsorshipFunded by a Chester College bursaryen
dc.language.isoenen
dc.publisherUniversity of Liverpool (University College Chester)en
dc.subjectfractional differential equationsen
dc.subjectdistributed order differential equationsen
dc.subjectmulti-term fractional differential equationsen
dc.titleThe numerical solution of fractional and distributed order differential equationsen
dc.typeThesis or dissertationen
dc.type.qualificationnamePhDen
dc.type.qualificationlevelDoctoralen
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