A numerical algorithm for solving nonlinear delay Volterra integral equations by means of homotopy perturbation method

In this study, the homotopy perturbation method (HPM) is applied to solve a general class of nonlinear delay Volterra integral equations (DVIEs). The main feature of the HPM is that it deforms a difficult problem into a set of problems which are easier to solve. We use the HPM to provide an approximate solution for the desired nonlinear DVIE in terms of convergent series with easily computable components. In addition, Legendre polynomials are implemented to solve complicated integrals arising in computations. We show that using Legendre polynomials reduces the volume of computations and runtime of the method. Finally, several numerical experiments are given to illustrate the pertinent features of the technique. The results demonstrate that the proposed method is of high accuracy, more convenient and efficient for solving nonlinear DVIEs.