In this article, the homotopy analysis method (HAM) for obtaining the analytical solution of the inverse parabolic problem and computing the unknown time-dependent parameter is introduced. The series solution is developed and the recurrence relations are given explicitly. Special attention is given to satisfy the convergence of the proposed method. A comparison of HAM with the variational iteration method is made. In the HAM, we use the auxiliary parameter ~ to control with a simple way in the convergence region of the solution series. Applying this method with several
Khader, M. M.
Analytical solution for determination the control parameter in the inverse parabolic equation using HAM,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 12,
2, Article 27.
Available at: https://digitalcommons.pvamu.edu/aam/vol12/iss2/27