Variational iteration method for inverse problem of diffusion equation

摘要

In this work, the solution of an inverse problem concerning a diffusion equation with source control parameters is presented. 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 variational iteration method is used for solving an inverse parabolic problem and computing an unknown time-dependent parameter. In this method, the solution is calculated in the form of a convergent series with an easily computable component. This approach does not need linearization, weak nonlinearity assumptions or perturbation theory. The results show applicability, accuracy and efficiency of VIM in solving inverse problems of parabolic type. It is predicted that VIM can be widely applied in science and engineering problems.