Journal of East China Normal University(Natural Sc ›› 2008, Vol. 2008 ›› Issue (3): 12-20.

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Singularly perturbed BVP for third nonlinear ODE(Chinese)

CHEN Li-hua1,2, XU Jie2, NI Ming-kang2,3   

  1. 1. Math ematics and Computer Science Department, Fuqing Branch of Fujian Normal University, Fujian 350300, China;2. Department of Mathematics, East China Normal University, Shanghai 200062, China;3. SJTU Section, Computational Science Division, E-Institute of Shanghai Universities, Shanghai 200030, China
  • Received:2007-06-15 Revised:2007-12-07 Online:2008-05-25 Published:2008-05-25
  • Contact: NI Ming-kang

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Abstract:

This paper studied a kind of BVP of nonlinear third order singularly perturbed equations by boundary layer function method. When gy′>0, at first, the problem was turned to a BVP of equivalent Tikhonov system. Then the asymptotic solution of doubly boundary layer for the system was constructed, and the character of exponential decay for all boundary functions was proved. Finally the main results of this paper: existence and uniqueness of solution and estimation of remainder for the problem are given. When gy′<0, in general, there is no solution to this problem.

Key words: boundary functions, invariant manifold, asymptotic analysis, singular perturbation, boundary functions, invariant manifold, asymptotic analysis

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