STABILITY OF HOMOTOPY PERTURBATION TECHNIQUE FOR AN INVERSE DIFFUSION PROBLEM

In this paper, a one-dimensional nonlinear inverse diffusion problem with nonlinear diffusivity term is considered. In the problem the values of function is unknown on some parts of domains boundary. By using the finite difference method and discretizing the time variable, the partial differential equation converts to a system of nonlinear ordinary differential equations. Consequently, by applying the homotopy perturbation technique, an approximate solution will be found at discrete times . Then some necessary conditions for convergence and stability of numerical scheme and, the upper bound of error for the solution of the problem is yield. Finally, a numerical experiment is given.