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Liao, Shijun

An optimal homotopy-analysis approach for strongly nonlinear differential equations. (English) Zbl 1222.65088

Commun. Nonlinear Sci. Numer. Simul. 15, No. 8, 2003-2016 (2010).
Summary: 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.

Cited in 2 Reviews
Cited in 162 Documents

MSC:

65L99 Numerical methods for ordinary differential equations
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
34A45 Theoretical approximation of solutions to ordinary differential equations

Keywords:

optimal homotopy-analysis method; nonlinear; analytic approximation; series solution
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\textit{S. Liao}, Commun. Nonlinear Sci. Numer. Simul. 15, No. 8, 2003--2016 (2010; Zbl 1222.65088)
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References:

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