Analytical methods for an elliptic singular perturbation problem in a circle

Authors:
N. M. Temme
Affiliations:
Centrum voor Wiskunde en Informatica (CWI), Kruislaan 413, 1098 SJ Amsterdam, The Netherlands
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

We consider an elliptic perturbation problem in a circle by using the analytical solution that is given by a Fourier series with coefficients in terms of modified Bessel functions. By using saddle point methods we construct asymptotic approximations with respect to a small parameter. In particular we consider approximations that hold uniformly in the boundary layer, which is located along a certain part of the boundary of the domain.