dc.contributor.advisor Yan, Yubin en_GB dc.contributor.author Nwajeri, Kizito U. * dc.date.accessioned 2013-07-09T12:19:50Z dc.date.available 2013-07-09T12:19:50Z dc.date.issued 2012-09 dc.identifier.uri http://hdl.handle.net/10034/295582 dc.description.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. dc.language.iso en en dc.publisher University of Chester en dc.subject fractional differential equations en_GB dc.subject ordinary differential equations en_GB dc.subject finite difference method en_GB dc.subject stability regions en_GB dc.subject Mittag-Leffler function en_GB dc.subject Riemann-Liouville fractional derivative en_GB dc.subject Caputo fractional derivative en_GB dc.title Stability regions of numerical methods for solving fractional differential equations en_GB dc.type Thesis or dissertation en dc.type.qualificationname MSc en dc.type.qualificationlevel Masters Degree en html.description.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.
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