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Application of the optimal homotopy asymptotic method to squeezing flow. (English) Zbl 1198.76095

Comput. Math. Appl. 59, No. 12, 3858-3866 (2010); correction ibibd. 60, No. 9, 2724 (2010).
Summary: Axisymmetric flow of two-dimensional incompressible fluids is studied. The Optimal Homotopy Asymptotic Method (OHAM) is applied to derive a solution of the reduced fourth-order nonlinear boundary value problem. For comparison, the same problem is also solved by the Perturbation Method (PM), the Homotopy Perturbation Method (HPM) and the Homotopy Analysis Method (HAM). OHAM is parameter free and provides better accuracy at lower order of approximation. Moreover we can easily adjust and control the convergence region. As a result it is concluded that the new technique, OHAM, shows fast convergence, simplicity of application and efficiency.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
65L99 Numerical methods for ordinary differential equations
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References:

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