Jha, Anuradha and Kadalbajoo, Mohan K (2015) A robust layer adapted difference method for singularly perturbed two-parameter parabolic problems. In: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 92 (6). pp. 1204-1221.
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A finite difference method for a time-dependent singularly perturbed convection-diffusion-reaction problem involving two small parameters in one space dimension is considered. We use the classical implicit Euler method for time discretization and upwind scheme on the Shishkin-Bakhvalov mesh for spatial discretization. The method is analysed for convergence and is shown to be uniform with respect to both the perturbation parameters. The use of the Shishkin-Bakhvalov mesh gives first-order convergence unlike the Shishkin mesh where convergence is deteriorated due to the presence of a logarithmic factor. Numerical results are presented to validate the theoretical estimates obtained.
| Item Type: | Journal Article |
|---|---|
| Publication: | INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS |
| Publisher: | TAYLOR & FRANCIS LTD |
| Keywords: | 65M12; 65M06; uniform convergence; Shishkin-Bakhvalov mesh; upwind method; two parameters; singular perturbations; unsteady problem |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 01 Apr 2015 12:08 |
| Last Modified: | 01 Apr 2015 12:08 |
| URI: | http://eprints.iisc.ac.in/id/eprint/51123 |
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