This paper is concerned with multiple solutions of a singular nonlinear boundary value problem (BVP) on the interval [0, 1], which arises in a study of the laminar flow in a porous pipe with an expanding.or contracting wall. For the singular nonlinear BVP, the correct boundary conditions are derived to guarantee that its linearization has a unique smooth solution. Then a numerical technique is proposed to find all possible multiple solutions. For the suction-driven pipe flow with the expanding wall (e.g. alpha = 2), we find a new solution numerically and classify it as a type VI solution. The computed results agree well with what can be obtained by the bifurcation package AUTO. In addition, we also construct asymptotic solutions for a few cases of parameters, which agree well with numerical solutions. These serve as validations of our numerical results. Thus we believe that the numerical technique designed in the paper is reliable, and may be further applied to solve a variety of nonlinear equations that arise from other flow problems. (C) 2016 Elsevier B.V. All rights reserved.
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Hunan First Normal Univ, Dept Math, Changsha 410205, Hunan, Peoples R China
Univ Helsinki, Dept Math & Stat, FI-00014 Helsinki, FinlandHunan First Normal Univ, Dept Math, Changsha 410205, Hunan, Peoples R China
Yang, Xuxin
Wang, Weibing
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Hunan Univ Sci & Technol, Dept Math, Xiangtan 411201, Hunan, Peoples R ChinaHunan First Normal Univ, Dept Math, Changsha 410205, Hunan, Peoples R China
Wang, Weibing
Shen, Jianhua
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Hangzhou Normal Univ, Dept Math, Hangzhou 310036, Zhejiang, Peoples R ChinaHunan First Normal Univ, Dept Math, Changsha 410205, Hunan, Peoples R China