An efficient iterative method based on Laplace transform or solving a class of nonlinear Volterra integral equations of the first kind

In this paper, an efficient method is proposed to solve a class of nonlinear volterra inte- gral equations of the first kind. The idea is based on converting nonlinear Volterra integral equations of the first kind into linear Volterra integral equations of the second kind. We apply homotopy perturbation transform method and two-step Laplace decomposition algorithm to solving the Volterra integral equations of the second kind. Numerical examples are given to illustrate efficiency and accuracy of the present method. Comparison with numerical results also been done.