Homotopy perturbation method for the hypersingular integral equations of the first kind

Abstract

Simple and efficient convex homotopy perturbation method (HPM) is presented to obtain an approximate solution of hyper-singular integral equations of the first kind. Convergence and error estimate of HPM are obtained. Three numerical examples were provided to verify the effectiveness of the HPM. Comparisons with reproducing kernel method (Chen et al., 2011) for the same number of iteration is also presented. Numerical examples reveal that the convergence of HPM can still be achieved for some problems even if the condition of convergence of HPM is not satisfied. MSC: 65R20, 45E05, Keywords: Homotopy perturbation method, Hypersingular integral, Numerical method, Convergence