Convergence and error estimation of homotopy perturbation method for Fredholm and Volterra integral equations

In this paper an application of the homotopy perturbation method for solving Fredholm and Volterra integral equations of the second kind is presented. Discussed method consists in constructing the functional series, sum of which determines the function giving the solution of considered problem. Conditions under which the constructed series is convergent are formulated and proved in the paper. In general, the composed series is rather fast convergent, thanks to which calculation of few first terms ensures a very good approximation of the sought solution. Estimation of errors of approximate solution obtained by taking the partial sum of the series is also elaborated in the paper.