Open AccessThe Essence of the Variational Iteration Method and the Homotopy Analysis Method Is Different
Author(s) -
Mustafa Türkyılmazoğlu,
AUTHOR_ID
Publication year - 2021
Publication title -
journal of mathematical sciences : advances and applications
Language(s) - English
Resource type - Journals
ISSN - 0974-5750
DOI - 10.18642/jmsaa_7100122169
Subject(s) - homotopy analysis method , mathematics , simple (philosophy) , homotopy , convergence (economics) , homotopy perturbation method , assertion , variational analysis , calculus (dental) , computer science , pure mathematics , medicine , philosophy , dentistry , epistemology , economics , programming language , economic growth
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.