Communications in Numerical Analysis
Volume 2013 (2013), Article ID cna-00139, 14 Pages
Analytic approximate solution for the Bratu's problem by optimal homotopy analysis method
Hany N. Hassan1 *, Mourad S. Semary1
1Department of Basic Science, Faculty of Engineering at Benha, Benha University, Benha 13512, Egypt
* Corresponding author. Email address: firstname.lastname@example.org; Tel: +201225839389
Received: 31 March 2012; Accepted: 04 January 2013
Copyright © 2013 Hany N. Hassan and Mourad S. Semary. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In This paper, we present analytic approximate solutions for Bratu's problem with high accuracy for different values of \lambda. We solve this nonlinear problem without any approximations or transformation in the problem and we successfully obtain the two branches of solutions for different values \lambda using homotopy analysis method. A new efficient approach is proposed to obtain the optimal value of convergence controller parameter \hbar to guarantee the convergence of the obtained series solution.
Keywords: Optimal homotopy analysis method; Bratu's problem; Series solutions; Two boundary value problem; Multiple solutions.
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