Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9506809 | Applied Mathematics and Computation | 2005 | 19 Pages |
Abstract
The objective of this paper is to construct some high order uniform numerical methods to solve linear reaction-diffusion singularly perturbed problems. First, for 1D elliptic problems, based on the central finite difference scheme, a new HODIE method is defined on a piecewise uniform Shishkin mesh. Using this HODIE scheme jointly with a two stage SDIRK method, we solve a 1D parabolic singularly perturbed problem. In both cases we prove that the methods are third-order uniform convergent in the maximum norm. Finally, for a 2D parabolic problem of the same type, we show numerically that the combination of the HODIE scheme with a fractional step RK method gives again a third-order uniform convergent scheme.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
C. Clavero, J.L. Gracia,