An hp-version of the discontinuous Galerkin time-stepping method for nonlinear second-order delay differential equations with vanishing delays
An hp-version of the discontinuous Galerkin time-stepping method for nonlinear second-order delay differential equations with vanishing delays
复制标题
用于求解时滞消失的非线性二阶时滞微分方程的不连续伽辽金时间步进方法的 hp 版本
DOI：
10.1016/j.cam.2019.112348
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发表时间：
2020-01
影响因子：
2.4
通讯作者：
Yi Lijun
中科院分区：
文献类型：
--
作者：
Wei Yichen;Sun Tao;Yi Lijun
We present and analyze an h p-version of the discontinuous Galerkin (DG) time-stepping method for nonlinear second-order delay differential equations with vanishing delays. We derive a priori error bounds in the L 2-and L∞-norm that are fully explicit with respect to the local time steps, the local approximation orders, and the local regularity of the exact solution. We further prove that the h p-DG scheme based on geometrically refined time steps and on linearly increasing approximation orders attains exponential rates of convergence for analytic solutions with start-up singularities. Moreover, we also propose an h p-DG scheme for the state dependent delay differential equations. We illustrate the theoretical results with a series of numerical experiments.
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