Article ID: | iaor20126114 |
Volume: | 155 |
Issue: | 1 |
Start Page Number: | 252 |
End Page Number: | 272 |
Publication Date: | Oct 2012 |
Journal: | Journal of Optimization Theory and Applications |
Authors: | Kaushik Aditya, Sharma Manju |
Keywords: | approximation, differential equations |
We consider the numerical approximation of a singularly perturbed time delayed convection diffusion problem on a rectangular domain. Assuming that the coefficients of the differential equation be smooth, we construct and analyze a higher order accurate finite difference method that converges uniformly with respect to the singular perturbation parameter. The method presented is a combination of the central difference spatial discretization on a Shishkin mesh and a weighted difference time discretization on a uniform mesh. A priori explicit bounds on the solution of the problem are established. These bounds on the solution and its derivatives are obtained using a suitable decomposition of the solution into regular and layer components. It is shown that the proposed method is