Comments on “A one-step optimal homotopy analysis method for nonlinear differential equations”
Comments on “A one-step optimal homotopy analysis method for nonlinear differential equations”
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DOI：
10.1016/j.cnsns.2010.01.038
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发表时间：
2010-11
影响因子：
3.9
通讯作者：
V. Marinca;N. Herisanu
中科院分区：
文献类型：
--
作者：
V. Marinca;N. Herisanu
上述文章存在一些根本性的错误和误解，并得出了错误的结论。由于不正确地应用了最优同伦渐近方法（OHAM）， Niu和Wang得出了错误的结论，即这种方法在实践中效率不高，因为它对高阶逼近很耗时。我们在他们的论文中强调了一些明显的错误和误解的存在，我们证明了OHAM在实践中是非常有效的，因为我们只使用一阶近似就解决了Niu和Wang分析的三个例子，得到了准确的结果。我们证明了OHAM不需要像Niu和Wang建议的那样高阶近似，我们表明OHAM的主要优势是它的快速收敛，这与Niu和Wang的假设相矛盾。
The above mentioned paper contains some fundamental mistakes and misinterpretations along with a false conclusion. Applying the optimal homotopy asymptotic method (OHAM) in an incorrect manner, Niu and Wang have drawn the false conclusion that this approach is not efficient in practice because it is time-consuming for high-order of approximation. We emphasized the presence of some evident mistakes and misinterpretations in their paper and we proved that OHAM is very efficient in practice since we solved all three examples analyzed by Niu and Wang using only the first-order of approximation, which yields accurate results. We demonstrate that OHAM does not need high-orders of approximation as Niu and Wang suggests and we show that the main strength of OHAM is its rapid convergence, contradicting Niu and Wang’s assumption.