ABSTRACT

In this paper, we investigate how many convergence orders of discontinuous Galerkin (DG) method for numerically solving neutral delay differential equations (NDDEs). Although discontinuous behaviour may occur in the derivatives of the exact solution at every breaking point, it is shown that the convergence order of the p-degree DG solution at the mesh points and characteristic points can achieve $\mathcal{O}(h^{2p+1})$ and $\mathcal{O}(h^{p+2})$, respectively. Numerical examples are also reported to confirm the theoretical results.

中文翻译：

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中性延迟微分方程间断Galerkin方法的超收敛

摘要

在本文中，我们研究了用于数值求解中性延迟微分方程 (NDDE) 的不连续伽辽金 (DG) 方法的收敛阶数。尽管精确解的导数在每个断点处都可能出现不连续行为，但证明了网格点和特征点处p度DG解的收敛阶数可以达到$\mathcal{哦}(H^{2磷+1})$ 和 $\mathcal{哦}(H^{磷+2})$， 分别。还报告了数值例子以证实理论结果。