论文标题
在适应网格上的延迟方程的单片操作员的分段离散化
Piecewise discretization of monodromy operators of delay equations on adapted meshes
论文作者
论文摘要
通常将延迟方程的周期解作为适合解决方案曲线的网格上的连续分段多项式近似。在实际计算中，这会影响线性化系统（系数）的规律性，进而影响通过近似Floquet乘数来评估局部稳定性的有效性。为了克服这个问题，当通过搭配计算乘数时，离散化网格应包括计算出的周期性解决方案的分段改编网格。通过引入现有伪谱技术的分段版本，我们可以解释原因，并在实验上表明，这种选择在存在强的网格适应性或非平凡的乘数的情况下至关重要，而这些乘数的特征函数的曲线与周期解决方案无关。
Periodic solutions of delay equations are usually approximated as continuous piecewise polynomials on meshes adapted to the solutions' profile. In practical computations this affects the regularity of the (coefficients of the) linearized system and, in turn, the effectiveness of assessing local stability by approximating the Floquet multipliers. To overcome this problem when computing multipliers by collocation, the discretization grid should include the piecewise adapted mesh of the computed periodic solution. By introducing a piecewise version of existing pseudospectral techniques, we explain why and show experimentally that this choice is essential in presence of either strong mesh adaptation or nontrivial multipliers whose eigenfunctions' profile is unrelated to that of the periodic solution.
