On a singular perturbation problem with two second-order turning points

Authors:
Heping Yang
Affiliations:
Department of Mathematics, Normal College, Shenzhen University, Shenzhen, Guangdong, PR China
Venue:
Journal of Computational and Applied Mathematics - Special issue: International conference on mathematics and its application
Year:
2006

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Abstract

In this paper, we study the singular perturbation problem εp(x)uxx + 2(x-a)(b-x)q(x)ux-2su=0, 0xabp(x) and q(x) are sufficiently smooth and strictly positive functions. The main feature of this equation is that there are two second-order turning points in the interval (0, 1). Based on the rigorous results on singular perturbation problems with one second-order turning point in our previous work, we obtain a uniform asymptotic approximation for the general solution of the above equation by means of a matching technique.