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An optimal homotopy-analysis approach for strongly nonlinear differential equations
- Source :
-
Communications in Nonlinear Science & Numerical Simulation . Aug2010, Vol. 15 Issue 8, p2003-2016. 14p. - Publication Year :
- 2010
-
Abstract
- Abstract: 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. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 10075704
- Volume :
- 15
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Communications in Nonlinear Science & Numerical Simulation
- Publication Type :
- Periodical
- Accession number :
- 48221428
- Full Text :
- https://doi.org/10.1016/j.cnsns.2009.09.002