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

MSC:
65L99Numerical methods for ODE
34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)
34A45Theoretical approximation of solutions of ODE