Reply to “Comments on ‘A one-step optimal homotopy analysis method for nonlinear differential equations”’. (English) Zbl 1222.65093

Wang, Chun; Niu, Zhao

Commun. Nonlinear Sci. Numer. Simul. 15, No. 11, 3740-3743 (2010).

Summary: V. Marinca and N. Herişanu [ibid. 15, No. 11, 3735–3739 (2010; Zbl 1222.65089)] made some comments on our paper [ibid. 15, No. 8, 2026–2036 (2010; Zbl 1222.65091)] 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.

MSC:

65L99

Numerical methods for ordinary differential equations

Keywords:

optimal homotopy analysis method; optimal homotopy asymptotic method; nonlinear differential equations

Citations:

Zbl 1222.65089; Zbl 1222.65091

Software:

Mathematica

References:

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