Some Notes on the Convergence Control Parameter in the Framework of the Homotopy Analysis Method

Volume 9, Issue 2, pp 103-110 http://dx.doi.org/10.22436/jmcs.09.02.03

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Authors

Jamshid Saeidian - Faculty of Mathematical Sciences and Computer, Kharazmi University, 50 Taleghani avenue, Tehran 1561836314, Iran. Shahnam Javadi - Faculty of Mathematical Sciences and Computer, Kharazmi University, 50 Taleghani avenue, Tehran 1561836314, Iran.

Abstract

The convergence control parameter and the technique of \(c_0\)-curves is an unavoidable part of any homotopy analysis method work. The mathematical background of this parameter has been studied by other authors. Here we revisit this parameter and its essence; we mention that in some examples the parameter may fail to work. Also we give some comments in using the technique of \(c_0\)-curves and show, through examples, that a misusage may lead the user to wrong results.

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Keywords

• Homotopy analysis method
• Convergence-control parameter
• Technique of \(c_0\)-curves.

MSC

•  65H99
•  35A25
•  35C10

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