Document Type
Article
Rights
This item is available under a Creative Commons License for non-commercial use only
Disciplines
Applied mathematics
Abstract
A class of nonlinear singularly perturbed interior layer problems is examined in this paper. Solutions exhibit an interior layer at an a priori unknown location. A numerical method is presented that uses a piecewise uniform mesh refined around approximations to the first two terms of the asymptotic expansion of the interior layer location. The first term in the expansion is used exactly in the construction of the approximation which restricts the range of problem data considered. The method is shown to converge point-wise to the true solution with a first order convergence rate (overlooking a logarithmic factor) for sufficiently small values of the perturbation parameter. A numerical experiment is presented to demonstrate the convergence rate established.
DOI
http://doi.org10.21427/jvsj-rn55
Recommended Citation
Quinn, J. (2014). A numerical method for a nonlinear singularly perturbed interior layer problem using an approximate layer location. Journal of Computational and Applied Mathematics doi :10.21427/jvsj-rn55
Publication Details
January 2015: Article is in submission to Journal of Computational and Applied Mathematics .