期刊
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
卷 15, 期 8, 页码 2003-2016出版社
ELSEVIER
DOI: 10.1016/j.cnsns.2009.09.002
关键词
Optimal homotopy-analysis method; Nonlinear; Analytic approximation; Series solution
类别
资金
- National Natural Science Foundation of China [10872129]
- State Key Lab of Ocean Engineering [GKZD010002]
In this paper, an optimal homotopy-analysis approach is described by means of the nonlinear Blasius equation as an example. This optimal approach contains at most three convergence-control parameters and is computationally rather efficient. A new kind of averaged residual error is defined, which can be used to find the optimal convergence-control parameters much more efficiently. It is found that all optimal homotopy-analysis approaches greatly accelerate the convergence of series Solution. And the optimal approaches with one or two unknown convergence-control parameters are strongly suggested. This optimal approach has general meanings and can be used to get fast convergent series Solutions of different types of equations with strong nonlinearity. (C) 2009 Elsevier B.V. All rights reserved.
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