Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 14, Issue 12, Pages 4078-4089Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2009.03.008
Keywords
Homotopy Analysis Method; Nonlinear differential equations; Series solutions; Perturbation methods
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The Homotopy Analysis Method of Liao [Liao SJ. Beyond perturbation: introduction to the Homotopy Analysis Method. Boca Raton: Chapman & Hall/CRC Press; 20031 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. (C) 2009 Elsevier B.V. All rights reserved.
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