Magister Scientiae - MSc / Efficient numerical approaches for parameter dependent problems have been an inter-
esting subject to numerical analysts and engineers over the past decades. This is due
to the prominent role that these problems play in modeling many real life situations
in applied sciences. Often, the choice and the e ciency of the approaches depend on
the nature of the problem to solve. In this work, we consider the general linear first-order singularly perturbed Volterra integro-differential equations (SPVIDEs). These
singularly perturbed problems (SPPs) are governed by integro-differential equations
in which the derivative term is multiplied by a small parameter, known as "perturbation parameter". It is known that when this perturbation parameter approaches
zero, the solution undergoes fast transitions across narrow regions of the domain
(termed boundary or interior layer) thus affecting the convergence of the standard
numerical methods. Therefore one often seeks for numerical approaches which preserve stability for all the values of the perturbation parameter, that is "numerical
methods. This work seeks to investigate some "numerical methods that have been
used to solve SPVIDEs. It also proposes alternative ones. The various numerical
methods are composed of a fitted finite difference scheme used along with suitably
chosen interpolating quadrature rules. For each method investigated or designed, we
analyse its stability and convergence. Finally, numerical computations are carried
out on some test examples to con rm the robustness and competitiveness of the
proposed methods.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:uwc/oai:etd.uwc.ac.za:11394/5669 |
| Date | January 2017 |
| Creators | Iragi, Bakulikira |
| Contributors | Munyakazi, Justin Bazimaziki |
| Publisher | University of the Western Cape |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Rights | University of the Western Cape |
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