Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10224200 | Journal of Computational and Applied Mathematics | 2019 | 22 Pages |
Abstract
In this paper, we investigate the local superconvergence of the discontinuous Galerkin (DG) solutions on quasi-graded meshes for nonlinear delay differential equations with vanishing delay. It is shown that the optimal order of the DG solution at the mesh points is O(h2m+1). By analyzing the supercloseness between the DG solution and the interpolation Î hu of the exact solution, we get the optimal order O(hm+2) of the DG solution at characteristic points. We then extend the convergence results of DG solutions to state dependent delay differential equations. Numerical examples are provided to illustrate the theoretical results.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Xiuxiu Xu, Qiumei Huang,