期刊
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
卷 14, 期 5, 页码 2144-2159出版社
ELSEVIER
DOI: 10.1016/j.cnsns.2008.06.013
关键词
Non-similarity; Boundary-layer; Series solution; Homotopy analysis method; Non-linear PDE with variable coefficient
类别
资金
- National Natural Science Foundation of China [10572095, 50739004]
- Program for Changjiang Scholars and Innovative Research Team in University [IRT0525]
- National 863 Plan Project of China [2006AA09Z354]
An analytic method for strongly non-linear problems, namely the homotopy analysis method (HAM), is applied to give convergent series Solution of non-similarity boundary-layer flows. As an example, the non-similarity boundary-layer flows over a Stretching flat sheet are used to show the validity of this general analytic approach. Without any assumptions of small/large quantities, the corresponding non-linear partial differential equation with variable coefficients is transferred into an infinite number of linear ordinary differential equations with constant coefficients. More importantly, an auxiliary artificial parameter is used to ensure the convergence of the series solution. Different from previous analytic results, our series solutions are convergent and valid for all physical variables in the whole domain of flows. This work illustrates that, by means of the homotopy analysis method, the non-similarity boundary-layer flows can be solved in a similar way like similarity boundary-layer flows. Mathematically, this analytic approach is rather general in principle and can be applied to solve different types of non-linear partial differential equations with variable coefficients in science and engineering. (C) 2008 Elsevier B.V. All rights reserved.
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