An efficient analytic approach for solving two-point nonlinear boundary value problems by homotopy analysis method

✍ Scribed by Hany N. Hassan; Magdy A. El-Tawil

• Publisher: John Wiley and Sons
• Year: 2011
• Tongue: English
• Weight: 539 KB
• Volume: 34
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1416

✦ Synopsis

Communicated by J. Cash

In this paper, we use homotopy analysis method (HAM) to solve two-point nonlinear boundary value problems that have at least one solution. The new approach provides the solution in the form of a rapidly convergent series with easily computable components using symbolic computation software. The scheme shows importance of choice of convergencecontrol parameter h to guarantee the convergence of the solutions of nonlinear differential equations. This scheme is tested on three nonlinear exactly solvable differential equations. Two of the examples are practical in science and engineering. The results demonstrate reliability, simplicity and efficiency of the algorithm developed.