期刊
RESULTS IN PHYSICS
卷 6, 期 -, 页码 20-25出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.rinp.2015.12.008
关键词
Optimal q-homotopy analysis method; Convergence-control parameter; Convection diffusion equation
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 h to guarantee the convergence of the obtained series solution. (C) 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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