کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6421823 | 1631827 | 2014 | 10 صفحه PDF | دانلود رایگان |
- We consider an adaptive grid approach to solve a singularly perturbed differential difference equation with small delay.
- The mesh is constructed adaptively by equidistributing a arc-length monitor function.
- We derive a first-order maximum norm a posteriori estimate for the full discretization scheme.
- 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.
Journal: Applied Mathematics and Computation - Volume 227, 15 January 2014, Pages 801-810