2012•Yingyong shuxue yu jisuan shuxue xuebaoRequires access
Second-order semi-linear singularly perturbed problems with nonlinear and infinite boundary value conditions
HU Yong-sheng
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Abstract
The second-order semi-linear singularly perturbed problems with nonlinear and infinite boundary value conditions are considered in this paper.By using the idea of boundary layer corrections,the exponential and algebraic boundary layer correction functions of the neighborhood of the left and right points are constructed,and hence,the asymptotic solution is obtained.According to the theory of differential inequalities,the existence of solutions,the uniform validity and the error estimation of the asymptotic solution are proved.The paper also focuses on the singular degree of the boundary value that can be allowed under certain stability conditions.A typical example is given to verify the correctness of the theoretical results and the high-precision for the asymptotic solution.