Current Proceedings on Technology
Yazarlar: Jalal Izadian, Sahebeh Salahshour, Soheil Salahshour
Konular:-
Anahtar Kelimeler:Volterra and Fredholm integral equations,Homotopy analysis method,Homotopy Perturbation Method, Numerical solution
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.