Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2011-05-31
Applied Mathematics and Computation 216 (2010) 1299-1303
Nonlinear Sciences
Exactly Solvable and Integrable Systems
5 pages
Scientific paper
The generalized Taylor expansion including a secret auxiliary parameter $h$ which can control and adjust the convergence region of the series is the foundation of the homotopy analysis method proposed by Liao. The secret of $h$ can't be understood in the frame of the homotopy analysis method. This is a serious shortcoming of Liao's method. We solve the problem. Through a detailed study of a simple example, we show that the generalized Taylor expansion is just the usual Taylor's expansion at different point $t_1$. We prove that there is a relationship between $h$ and $t_1$, which reveals the meaning of $h$ and the essence of the homotopy analysis method. As an important example, we study the series solution of the Blasius equation. Using the series expansion method at different points, we obtain the same result with liao's solution given by the homotopy analysis method.
No associations
LandOfFree
The essence of the homotopy analysis method does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The essence of the homotopy analysis method, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The essence of the homotopy analysis method will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-337754