APPLICATION OF ADOMAIN'S DECOMPOSITION METHOD AND HOMOTOPY PERTURBATION METHOD FOR SOLVING INTEGRAL EQUATIONS

Abstract

This research aims at learning the integral equations (linear or nonlinear) with special emphasis a Fredholm and Volterra integral equations. The research, also, aims at investigating different methods and techniques for solving these equations. Actually, the main objective of the research is learn Adomain decomposition method (and the modified one) applied in the two targeted integral equation, to compare this method with the others. In the first chapter, the researcher gave brief definitions for integral equations –as general and their classifications with much more elaboration to Fredholm and Volterra integral equations. In the second chapter the researcher explained to concept of solution of integral equation ,then , he introduced three of the well known methods and techniques used for solving integral equations: • The direct computation method • The successive substitution method • The successive approximation method

The researcher gave a brief explanation for each of the above mentioned methods and applied it every method Volterra and Fredholm integral equations accompanied by an illustrative examples. Chapter three is completely devoted for discussing the Adomain decomposition method and its modified form. He used it in solving Volterra and Fredholm integral equations. In the last chapter , the researcher discussed the Wavelet – Galerkin and Homotopy Perturbation methods compared with Adomain, s decomposition method .Then he applied these methods on the equations under investigation .Various examples were added for more illustrations. Finally, the researcher made tables comparing between the five methods at one side and Adomain decomposition method on the other side. At the end, the researcher concluded that Adomain decomposition methods have more advantages over the other (investigated) ones. .