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Extended homotopy perturbation method and computation of flow past a stretching sheet. (English) Zbl 1189.65156

Summary: We introduce an extended version of the homotopy perturbation method (HPM) for computing the steady flow of an incompressible, viscous fluid past a radially stretching sheet. In this version the independent variable is stretched by scaling it by a parameter that incorporates the homotopy parameter \(p\). The coefficients in the parameter are determined by requiring that the solutions obtained at each stage are free of secular terms. It is shown that the totally analytical solution developed by applying the extended version leads to a convergent sequence of homotopy solutions, the convergence of which can be accelerated by applying Shanks’ transformation.

MSC:

65L99 Numerical methods for ordinary differential equations
76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
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