论文标题
计算智障功能微分方程的定期解决方案的套在一起方法的收敛分析
Convergence analysis of collocation methods for computing periodic solutions of retarded functional differential equations
论文作者
论文摘要
我们分析了在[S. S. Maset，Numer。数学。 （2016）133（3）：525-555]，[S。 Maset，Siam J. Numer。肛门。 （2015）53（6）：2771--2793]和[S. Maset，Siam J. Numer。肛门。 （2015）53（6）：2794--2821]。我们严格地表明，作为边界价值问题的重新制定需要适当的无限尺寸边界周期性条件，以便进行此类分析。在这方面，我们还强调了该时期充当未知参数的作用，这至关重要，因为它与时间过程直接相关。最后，我们证明有限元方法是收敛的，而就频谱元素方法而言，我们将自己限制在评论这种方法的不可行性。
We analyze the convergence of piecewise collocation methods for computing periodic solutions of general retarded functional differential equations under the abstract framework recently developed in [S. Maset, Numer. Math. (2016) 133(3):525-555], [S. Maset, SIAM J. Numer. Anal. (2015) 53(6):2771--2793] and [S. Maset, SIAM J. Numer. Anal. (2015) 53(6):2794--2821]. We rigorously show that a reformulation as a boundary value problem requires a proper infinite-dimensional boundary periodic condition in order to be amenable of such analysis. In this regard, we also highlight the role of the period acting as an unknown parameter, which is critical since it is directly linked to the course of time. Finally, we prove that the finite element method is convergent, while we limit ourselves to commenting on the infeasibility of this approach as far as the spectral element method is concerned.
