A Procedure for Constructing the Solution of a Nonlinear Fredholm Integro-Differential Equation of Second Order

In this work, a large class of integro-differential equations, arising from the description heat transfer problems, is considered, particularly nonlinear equations. We propose procedure for constructing their solution in very simple and reliable way which only needed tool same one employed to solve linear second-order ordinary differential equation, subject Robin boundary conditions. Proofs convergence, existence, uniqueness are presented. Some special cases simulated illustrate proposed tools.