Abstract
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.