Solving the convection–diffusion equation by means of the optimal q-homotopy analysis method (Oq-HAM)

The main aim of this paper is to propose a new and simple algorithm namely the optimal q-homotopy analysis method (Oq-HAM), to obtain approximate analytical solutions of the convection diffusion (CD) equation. Comparison of Oq-HAM with the homotopy analysis method (HAM) and the homotopy perturbation method (HPM) is made. The results reveal that the Oq-HAM has more accuracy than the others. Finally, numerical example is given to illustrate the accuracy and stability of this method. Comparison of the approximate solution with the exact solutions shows that the proposed method is very efficient and computationally attractive. A new efficient approach is proposed to obtain the optimal value of convergence controller parameter ℏ to guarantee the convergence of the obtained series solution.