Analytical methods for an elliptic singular perturbation problem In a circle
Journal of Computational and Applied Mathematics , Volume 207 - Issue 2 p. 301- 322
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.
|singular perturbations, elliptic equations, boundary value problem, series solution, uniform asymptotic expansion.|
|Journal of Computational and Applied Mathematics|
|Special issue: Proceedings of the Conference in Honour of Dr. Nico Temme on the Occasion of his 65th birthday, Santander (Spain) 4-6 July 2005.|
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.