M.Sc. (Applied Mathematics) / A comparison between the recently developed spectral relaxation method (SRM) and the spectral local linearisation method (SLLM) is done for the first time in this work. Both spectral hybrid methods are employed in finding the solution to the non isothermal mass and heat balance model of a catalytic pellet boundary value problem (BVP) with finite mass and heat transfer resistance, which is a coupled system of singular nonlinear ordinary differential equations (ODEs). The SRM and the SLLM are applied, for the first time, to solve a problem with singularities. The solution by the SRM and the SLLM are validated against the results by bvp4c, a well known matlab built-in procedure for solving BVPs. Tables and graphs are used to show the comparison. The SRM and the SLLM are exceptionally accurate with the SLLM being the fastest to converge to the correct solution. We then construct a new spectral hybrid method which we named the spectral Adomian decomposition method (SADM). The SADM is used concurrently with the standard Adomian decomposition method (ADM) to solve well known models arising in fluid mechanics. These problems are the magneto hydrodynamic (MHD) Jeffery-Hamel flow model and the Darcy-Brinkman- Forchheimer momentum equations. The validity of the results by the SADM and ADM are verified by the exact solution and bvp4c solution where applicable. A simple alteration of the SADM is made to improve the performance.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:uj/uj:11638 |
| Date | 01 July 2014 |
| Creators | Mdziniso, Madoda Majahonkhe |
| Source Sets | South African National ETD Portal |
| Detected Language | English |
| Type | Thesis |
| Rights | University of Johannesburg |
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