Staff Members - Benha University
Analytic approximate solution for the Bratu's problem by optimal homotopy analysis method
Communications in Numerical Analysis • 2013
Publication Information
Authors
Hany N. Hassan; Mourad S. Semary
Keywords
Optimal homotopy analysis method , Bratu's problem, Series solutions, Two boundary value problem,
Multiple solutions.
Journal
Communications in Numerical Analysis
Publisher
Not Available
Volume
2013
Issue
Not Available
Pages
Not Available
publication.type
International
Paper Link
Not Available
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.
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.