| publication name | Analytic approximate solution for the Bratu's problem by optimal homotopy analysis method |
|---|---|
| Authors | Hany N. Hassan; Mourad S. Semary |
| year | 2013 |
| keywords | Optimal homotopy analysis method , Bratu's problem, Series solutions, Two boundary value problem, Multiple solutions. |
| journal | Communications in Numerical Analysis |
| volume | 2013 |
| issue | Not Available |
| pages | Not Available |
| publisher | Not Available |
| Local/International | International |
| Paper Link | Not Available |
| Full paper | download |
| Supplementary materials | Not Available |
Abstract
In This paper, we present analytic approximate solutions for Bratu's problem with high accuracy for different values of λ. 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 λ using homotopy analysis method. 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.