Using homotopy analysis method for solving fredholm and volterra integral equations
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Date
2017-01-20
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Abstract
In this thesis,we focus on using the Homotopy Analysis Method (HAM) to Fred-
holm and Volterra integral equation of the second kind.The HAM is based on
homotopy,a fundamental concept in topology and di erential geometry.After the
classi cation of these integral equations ,we take a look at a review of integral
equation and Homotopy Analysis Method (HAM) coupled with theories and def-
initions of homotopy theory.The description of the method (HAM) to solve Fred-
holm and Volterra integral equations is analyzed.In this method one constructs
a continuous mapping of an initial guess approximation to the exact solution of
considered equation.Application of the HAM to some examples of Fredholm and
Volterra integral equations is carried out together with the auxiliary parameter }
,which controls the convergence rate of the series solution. After the realization
of the exact solution of the various considered equations, MATLAB,a computa-
tional software is used to produce graphs of the various exact solutions which
shows the convergence of the series solution.
Description
A thesis submitted to the Department of Mathematics,
Kwame Nkrumah University of Science and Technology in
partial fulfillment of the requirement for the Degree
of Master of Philosophy in Pure Mathematics, 2016