Using homotopy analysis method for solving fredholm and volterra integral equations

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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.
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