Semi Exact Solutions for Bi-Harmonic EquationsUsing Homotopy Analysis Method

Citation:
Khader, S. N. H. M. M., "Semi Exact Solutions for Bi-Harmonic EquationsUsing Homotopy Analysis Method", World Applied Sciences Journal, 2011.

Abstract:

In this article, the homotopy analysis method (HAM) for obtaining semi analytical solutions of biharmonicequations is introduced. Series solutions of the problem under consideration are developed by meansof HAM and the recurrence relations are given explicitly. The initial approximation can be freely chosen withpossible unknown constants which can be determined by imposing the boundary and initial conditions. Thenumerical examples show the rapid convergence of the series constructed by this method to the exact solution.Moreover, this technique does not require any discretization, linearization or small perturbations. Test problemshave been considered to ensure that HAM is accurate and efficient compared with the variational iterationmethod (VIM).

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