A new analytical technique to solve Fredholm's integral equations (Q621780)

The homotopy analysis method is a well known tool for the theoretical approximation of various types of differential equations. In this paper, this analytical technique is applied to a class of Fredholm integral equations. In line with the results obtained when applying the approach to other types of equations, the authors prove that the method converges to the exact solution on a certain set if it converges at all. The authors neither provide information about the size of the set where convergence can be observed nor do they give sufficient conditions that assert convergence. The Adomian decomposition is shown to be a special case of the method (and is known to suffer from the same deficiencies).