Methods of moving boundary in heat conduction direct problem

The initial boundary value problem for parabolic equation with Neumann boundary condition is a kind of classical problem in partial differential equations. The direct problem is to determine the temperature field from given initial and boundary conditions. Compared with the fixed boundary problem, there is another boundary problem of moving boundary. In this paper we use the artificial boundary to solve the moving boundary problem. Potential theory method is used to deal with this problem, compared with the method of difference already. Numerical results are given to support the proposed schemes and to give the compare of the two methods.