Stability regions of numerical methods for solving fractional differential equations

Hdl Handle:
http://hdl.handle.net/10034/295582
Title:
Stability regions of numerical methods for solving fractional differential equations
Authors:
Nwajeri, Kizito U.
Abstract:
This dissertation deals with proper consideration of stability regions of well known numerical methods for solving fractional differential equations. It is based on the algorithm by Diethelm [15], predictor-corrector algorithm by Garrappa [31] and the convolution quadrature proposed by Lubich [3]. Initially, we considered the stability regions of numerical methods for solving ordinary differential equation using boundary locus method as a stepping stone of understanding the subject matter in Chapter 4. We extend the idea to the fractional differential equation in the following chapter and conclude that each stability regions of the numerical methods differs because of their differences in weights. They are illustrated by a number of graphs.
Advisors:
Yan, Yubin
Publisher:
University of Chester
Publication Date:
Sep-2012
URI:
http://hdl.handle.net/10034/295582
Type:
Thesis or dissertation
Language:
en
Appears in Collections:
Masters Dissertations

Full metadata record

DC FieldValue Language
dc.contributor.advisorYan, Yubinen_GB
dc.contributor.authorNwajeri, Kizito U.en_GB
dc.date.accessioned2013-07-09T12:19:50Z-
dc.date.available2013-07-09T12:19:50Z-
dc.date.issued2012-09-
dc.identifier.urihttp://hdl.handle.net/10034/295582-
dc.description.abstractThis dissertation deals with proper consideration of stability regions of well known numerical methods for solving fractional differential equations. It is based on the algorithm by Diethelm [15], predictor-corrector algorithm by Garrappa [31] and the convolution quadrature proposed by Lubich [3]. Initially, we considered the stability regions of numerical methods for solving ordinary differential equation using boundary locus method as a stepping stone of understanding the subject matter in Chapter 4. We extend the idea to the fractional differential equation in the following chapter and conclude that each stability regions of the numerical methods differs because of their differences in weights. They are illustrated by a number of graphs.en_GB
dc.language.isoenen
dc.publisherUniversity of Chesteren
dc.subjectfractional differential equationsen_GB
dc.subjectordinary differential equationsen_GB
dc.subjectfinite difference methoden_GB
dc.subjectstability regionsen_GB
dc.subjectMittag-Leffler functionen_GB
dc.subjectRiemann-Liouville fractional derivativeen_GB
dc.subjectCaputo fractional derivativeen_GB
dc.titleStability regions of numerical methods for solving fractional differential equationsen_GB
dc.typeThesis or dissertationen
dc.type.qualificationnameMScen
dc.type.qualificationlevelMasters Degreeen
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