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In this paper, three types of parabolic inverse problems are solved by homotopy analysis method (HAM). In order to solve these types of problems, an overspecified boundary condition is given. There are advantages to using HAM, firstly it is independent of small/large physical parameters, there is always a guarantee of convergence; there is flexibility on the choice of base function and initial guess of solution and lastly there is great generality. The numerical results obtained from this method indicate high accuracy and a strong rate of convergence.

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In this paper we obtain the solution of one-phase inverse Stefan problem by homotopy analysis method. The distribution of temperature on the boundary such that () () t v t u = , 0 , along with the temperature distribution () t x u , are obtained. The moving front () t s is given as additional information. There are advantages to using the homotopy analysis method (HAM), firstly it is independent of small/large physical parameter, there is always a guarantee of convergence; there is flexibility on the choice of base function and the initial guess of solution and lastly there is great generality. The numerical results obtained will show high accuracy and a strong rate of convergence.

In this paper the solution procedure in obtaining two times -dependent coefficients in a one dimensional partial differential equation and the temperature distribution is discussed and solved. We use the homotopy analysis method to obtain the solution of both the unknown coefficients and the temperature distribution. The solutions to the unknown coefficients are obtained by reducing our problem to a system of equations at every time step. There are advantages to using HAM, firstly it is independent of small/large physical parameters, there is flexibility on the choice of base function and initial guess of solution and lastly there is great generality. The results obtained from this method shows high accuracy, computational efficiency and a strong rate of convergence.