Application of HPM for determination of an unknown function in a semi-linear parabolic equation

Abstract

In this work, the homotopy perturbation method, a powerful technique, is applied to obtain an unknown time-dependent function in a semi-linear parabolic equation with given initial and boundary conditions. This kind of problem plays a very important role in many branches of science and engineering. Using the homotopy perturbation method a rapid convergent sequence can be constructed which tends to the exact solution of the problem. Some examples are presented to illustrate the strength of the method.