| Abstract: |
| In this talk we shall present the hp version continuous Galerkin and collocation methods for nonlinear delay differential equations with vanishing delays. We derive several a priori error estimates that are completely explicit with respect to the local time steps, the local polynomial degrees, and the local regularity of the exact solution. In particular, we show that the hp version continuous Galerkin scheme based on geometrically refined time steps and on linearly increasing approximation orders achieves exponential rates of convergence for solutions with start-up singularities. The theoretical results are illustrated by some numerical experiments. |
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