Yan, YubinNwajeri, Kizito U.2013-07-092013-07-092012-09http://hdl.handle.net/10034/295582This 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.enfractional differential equationsordinary differential equationsfinite difference methodstability regionsMittag-Leffler functionRiemann-Liouville fractional derivativeCaputo fractional derivativeThesis or dissertation