Determination of two-time dependent coefficients in a parabolic partial differential equation by homotopy analysis method - Onyejekwe, Ogugua (International Journal of Applied Mathematical Research, 2014)
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.   Keywords: Heat Equation, Homotopy Analysis Method, Inverse Problem, Time - Dependent Diffusion Coefficients.