Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: Mustafa Turkyilmazoglu
Pages: [47] - [63]
Received Date: February 7, 2021; Revised April 7, 2021
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100122169
The recently published paper “The variational iteration method is a special case of the homotopy analysis method” by Robert A. Van Gorder [1], weakly pointed out that the variational iteration method and all of its optimal analogues are specific cases of the more general homotopy analysis method. This assertion was not truly supported by a rigorous mathematical proof, nor by an accessible example from the attributed papers. In this brief, we refute the author's claim by supplementing three simple examples, which do not indicate that the variational iteration method is a special case of the homotopy analysis method. This is justified by a Theorem to compute the rate of convergence of both methods.
homotopy analysis method, variational iteration method, comparison, convergence.
