In this paper, we outline the combined Laplace homotopy perturbation method (LHPM) for solving nonlinear Volterra-Fredholm integral equation with singular Volterra kernels. The accuracy of the proposed numerical method is examined by comparing with the exact solution in the examples. Also, the results demonstrate the efficiency of the presented method.

singular integral equation, linear and nonlinear Volterra-Fredholm integral equation, homotopy perturbation method, Carleman kernel, logarithmic kernel and Cauchy kernel.