Title

On The Selection Of Auxiliary Functions, Operators, And Convergence Control Parameters In The Application Of The Homotopy Analysis Method To Nonlinear Differential Equations: A General Approach

Keywords

Homotopy Analysis Method; Nonlinear differential equations; Perturbation methods; Series solutions

Abstract

The Homotopy Analysis Method of Liao [Liao SJ. Beyond perturbation: introduction to the Homotopy Analysis Method. Boca Raton: Chapman & Hall/CRC Press; 2003] has proven useful in obtaining analytical solutions to various nonlinear differential equations. In this method, one has great freedom to select auxiliary functions, operators, and parameters in order to ensure the convergence of the approximate solutions and to increase both the rate and region of convergence. We discuss in this paper the selection of the initial approximation, auxiliary linear operator, auxiliary function, and convergence control parameter in the application of the Homotopy Analysis Method, in a fairly general setting. Further, we discuss various convergence requirements on solutions. © 2009 Elsevier B.V. All rights reserved.

Publication Date

12-1-2009

Publication Title

Communications in Nonlinear Science and Numerical Simulation

Volume

14

Issue

12

Number of Pages

4078-4089

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.cnsns.2009.03.008

Socpus ID

67349169966 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/67349169966

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