This study seeks to develop a method that generalises the use of Adams-Bashforth to
solve or treat partial differential equations with local and non-local differentiation by
deriving a two-step Adams-Bashforth numerical scheme in Laplace space. The resulting
solution is then transformed back into the real space by using the inverse Laplace
transform. This is a powerful numerical algorithm for fractional order derivative. The
error analysis for the method is studied and presented. The numerical simulations of
the method as applied to the four-dimensional model, Caputo-Lu-Chen model and the
wave equation are presented.
In the analysis, the bifurcation dynamics are discussed and the periodic doubling processes
that eventually caused chaotic behaviour (butterfly attractor) are shown. The
related graphical simulations that show the existence of fractal structure that is characterised
by chaos and usually called strange attractors are provided.
For the Caputo-Lu-Chen model, graphical simulations have been realised in both integer
and fractional derivative orders. / Mathematical Sciences / M. Sc. (Applied Mathematics)
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:unisa/oai:uir.unisa.ac.za:10500/26398 |
| Date | 05 1900 |
| Creators | Sibiya, Abram Hlophane |
| Contributors | Goufo, Emile Franc Doungmo |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Dissertation |
| Format | 1 online resource (81 leaves) : color illustrations, color graphs, application/pdf |
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