Reply to “Comments on ‘A one-step optimal homotopy analysis method for nonlinear differential equations”’
✍ Scribed by Chun Wang; Zhao Niu
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 163 KB
- Volume
- 15
- Category
- Article
- ISSN
- 1007-5704
No coin nor oath required. For personal study only.
✦ Synopsis
Marinca et al.
[1] made some comments on our paper [2] and pointed out ''some fundamental mistakes and misinterpretations along with a false conclusion". Unfortunately, Marinca's comments are wrong. Here, we further reveal the essence of Marinca's approach, and point out the reason why their method is indeed time-consuming: their method is nothing more than a traditional method in approximation theory. Numerical results for a given example and related MATHEMATICA code are given to support our view-points.
📜 SIMILAR VOLUMES
In this paper, a one-step optimal approach is proposed to improve the computational efficiency of the homotopy analysis method (HAM) for nonlinear problems. A generalized homotopy equation is first expressed by means of a unknown embedding function in Taylor series, whose coefficient is then determi
The Homotopy Analysis Method of Liao [Liao SJ. Beyond perturbation: introduction to the Homotopy Analysis Method. Boca Raton: Chapman & Hall/CRC Press; 2003] has proven useful in obtaining analytical solutions to various nonlinear differential equations. In this method, one has great freedom to sele