On decoupled quasi-linearization methods for solving systems of nonlinear boundary value problems.

Abstract

In this dissertation, a comparative study is carried out on three spectral based numerical methods which are the spectral quasilinearization method (SQLM), the spectral relaxation method (SRM) and the spectral local linearization method (SLLM). The study is carried out by applying the numerical methods on systems of differential equations modeling uid ow problems. Residual error analysis is used in determining the speed of convergence, convergence rate and accuracy of the methods. In Chapter 1, all the terminologies and methods that are applied throughout the course of the study are introduced. In Chapter 2, the SRM, SLLM and SQLM are applied on an unsteady free convective heat and mass transfer on a stretching surface in a porous medium with suction/injection. In Chapter 3, the SRM, SLLM and SQLM are applied on an unsteady boundary layer ow due to a stretching surface in a rotating uid. In Chapter 4, the SRM, SLLM and SQLM are used to solve an unsteady three-dimensional MHD boundary layer ow and heat transfer over an impulsively stretching plate. The purpose of this study is to assess the performance of the spectral based numerical methods when solving systems of differential equations. The performance of the methods are measured in terms of computational efficiency (in terms of time taken to generate solutions), accuracy and rate of convergence. The ease of development and implementation of the associated numerical algorithms are also considered.