Approximate analytic solutions of nonlinear integral equations

This thesis is related with nonlinear integral equations, nonlinear systems of integral equations and integro-differential equations. The existence and uniqueness of these equations for Lipschitz continuous kernels are investigated. An analytic method based on He?s Homotopy Perturbation Method (HPM) for the solution of nonlinear integral equations and systems are studied and applied. This method is extended for nonlinear integro-differential equations. Moreover, some examples of the mathematics program, solutions are given by MATHEMATICA 7. The approximate solutions of these equations are compared with the analytic approximation methods such as Adomian Decomposition Method (ADM) and Taylor?Series Expansion Method. The comparison shows that the (HPM) is quite conform and efficient for solving nonlinear problems.