Solutions of the Volterra integro-differential equation.
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Date
2018
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Abstract
Integro-di erential equations has found extensive applications in the eld of engineering, sciences
and mathematical modelling of various physical and biological phenomena. In this thesis
we focus on the Volterra type integro-di erential equation which has been used to model biological
species co-existing, heat di usion, electromagnetic theory etc. In recent years much
research has focused on nding approximate solutions of the integro-di erential equation by
polynomial methods, speci cally focusing on the Lagrange collocation and piecewise cubic Hermite
collocation methods. A further aspect to the thesis will be on analytical methods, mainly
the applications of Lie group theory to the Volterra type equation. Lie group theory is one
of the most powerful methods applied to obtain solutions of di erential equations. We will
present the linear independent symmetries of the Volterra type equation of the rst and second
kind. In addition, we shall apply the Laplace transform and it's inverse to determine general
solutions for selected forms of kernel, speci cally those with convolution integrands.
Description
Master’s degree. University of KwaZulu-Natal, Durban.