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. .
