Abstract
Collocation with quadratic C 1-splines for a singularly perturbed reaction-diffusion problem in one dimension is studied. A modified Shishkin mesh is used to resolve the layers. The resulting method is shown to be almost second order accurate in the maximum norm, uniformly in the perturbation parameter. Furthermore, a posteriori error bounds are derived for the collocation method on arbitrary meshes. These bounds are used to drive an adaptive mesh moving algorithm. Numerical results are presented.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 35-55 |
| Number of pages | 21 |
| Journal | Numerical Algorithms |
| Volume | 61 |
| Issue number | 1 |
| DOIs | |
| State | Published - Sep 2012 |
| Externally published | Yes |
Bibliographical note
Funding Information:H. Zarin is supported by the Ministry of Education and Science of the Republic of Serbia under grant 174030.
Funding Information:
This publication has eminated from research conducted with support by the DAAD (grant no. 50740187) and the Ministry of Education and Science of the Republic of Serbia under grant “Collocation methods for singularly perturbed problems”.
Keywords
- A posteriori error estimation
- Reaction-diffusion problems
- Singular perturbations
- Spline collocation
- Spline interpolation