Fractional differential equations and numerical methods

Hdl Handle:
http://hdl.handle.net/10034/93746
Title:
Fractional differential equations and numerical methods
Authors:
Landy, Alan J.
Abstract:
The increasing use of Fractional Calculus demands more accurate arid efficient methods for the numerical solution of fractional differential equations. We introduce the concepts of Fractional Calculus and give the definitions of fractional integrals and derivatives in the Riemann-Liouville and Caputo forms. We explore three existing Numerical Methods of solution of Fractional Differential Equations. 1. Diethelm's Backward Difference Form (BDF) method. 2. Lubich's Convolution Quadrature method. 3. Luchko and Diethelm's Operational Calculus (using the Mittag-Lefner function) method. We present useful recursive expressions we developed to compute the Taylor Series coefficients in the Operational Calculus method. These expressions are used in the calculation of the convolution and starting weights. We compare their accuracy and performance of the numerical methods, and conclude that the more complex methods produce the more accurate results.
Advisors:
Ford, Neville J.
Publisher:
University of Chester
Publication Date:
22-Jun-2009
URI:
http://hdl.handle.net/10034/93746
Type:
Thesis or dissertation
Language:
en
Appears in Collections:
Masters Dissertations

Full metadata record

DC FieldValue Language
dc.contributor.advisorFord, Neville J.en
dc.contributor.authorLandy, Alan J.en
dc.date.accessioned2010-03-05T12:09:38Zen
dc.date.available2010-03-05T12:09:38Zen
dc.date.issued2009-06-22en
dc.identifier.urihttp://hdl.handle.net/10034/93746en
dc.description.abstractThe increasing use of Fractional Calculus demands more accurate arid efficient methods for the numerical solution of fractional differential equations. We introduce the concepts of Fractional Calculus and give the definitions of fractional integrals and derivatives in the Riemann-Liouville and Caputo forms. We explore three existing Numerical Methods of solution of Fractional Differential Equations. 1. Diethelm's Backward Difference Form (BDF) method. 2. Lubich's Convolution Quadrature method. 3. Luchko and Diethelm's Operational Calculus (using the Mittag-Lefner function) method. We present useful recursive expressions we developed to compute the Taylor Series coefficients in the Operational Calculus method. These expressions are used in the calculation of the convolution and starting weights. We compare their accuracy and performance of the numerical methods, and conclude that the more complex methods produce the more accurate results.en
dc.language.isoenen
dc.publisherUniversity of Chesteren
dc.subjectfractional differential equationsen
dc.titleFractional differential equations and numerical methodsen
dc.typeThesis or dissertationen
dc.type.qualificationnameMScen
dc.type.qualificationlevelMasters Degreeen
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