Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6421823 | Applied Mathematics and Computation | 2014 | 10 Pages |
â¢We consider an adaptive grid approach to solve a singularly perturbed differential difference equation with small delay.â¢The mesh is constructed adaptively by equidistributing a arc-length monitor function.â¢We derive a first-order maximum norm a posteriori estimate for the full discretization scheme.â¢A first-order rate of convergence, independent of the perturbation parameter and the small delay parameter, is established.
A singularly perturbed differential difference equation with small delay is discretized on an adaptive grid which is formed by equidistributing arc-length monitor function. We first derive first-order maximum norm a posteriori estimates for the full discretization scheme of these problems. Then a first-order rate of convergence, independent of the perturbation parameter and the small delay parameter, is established. Numerical results are provided that support our theoretical estimates.