Inverse problem of diffusion equation by He's homotopy perturbation method

Inverse problems of parabolic type arise from many fields of physics and play a very important role in various branches of science and engineering. In the last few years, considerable efforts have been expended in formulating accurate and efficient methods to solve these equations. In this research, the homotopy perturbation method is used for solving an inverse parabolic equation and computing an unknown time-dependent parameter. The homotopy perturbation technique is an analytical procedure for finding the solutions of differential equations which is based on the constructing of a homotopy with an imbedding parameter p is an element of [0, 1] that is considered as an 'expanding parameter'. In this paper, a very brief introduction to the applications of the used technique and its new development is given. The results of applying this procedure to the studied parabolic inverse problem show the high accuracy, simplicity and efficiency of the approach.