%0 Journal Article
%T Analytic approximate solution for the Bratu's problem by optimal homotopy analysis method
%A Hany N. Hassan
%A Mourad S. Semary
%J Communications in Numerical Analysis
%D 2013
%I International scientific publication and consulting services (ISPACS)
%R 10.5899/2013/cna-00139
%X 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.
%K "">Optimal homotopy analysis method
%K Bratu's problem
%K Series solutions
%K Two boundary value problem
%K Multiple solutions"/>
%U http://www.ispacs.com/journals/cna/2013/cna-00139/article.pdf