Özet:

Homotopy  Analysis Method (HAM) and Homotopy Perturbation Method (HPM) is known to  be two powerful tools  for solving many functional  equations such as ordinary  and partial differential   and integral equations. In this paper (HAM) is applied to solve linear Fredholm  and Volterra first and second kind integral equations, the deformation equations are solved analytically by using  MATLAB integration functions. Numerical techniques for solving deformation  equation  are also  applied using  interpolation methods  and Gaussian  integration. Auxiliary  parameter h is also used experimentally  to control  convergence of partial  sum of  series solution. Several  examples are tested  by  these  methods  and numerical results are  compared with  exact solution or  existing  numerical  results to demonstrate  the efficiency  of the methods. These methods can be generalized to non-linear Volterra and Fredholm integral equation. The analytical and numerical results show the performance and reliability of presented method.

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