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.

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Journal of Computational and Applied Mathematics

Temme, N.M. (2007). Analytical methods for an elliptic singular perturbation problem In a circle. Journal of Computational and Applied Mathematics, 207(2), 301–322.