在[S.马塞特，努默。（2016）133（3）：525-555]、[S. Maset，SIAM J. Numer. Anal.（2015）53（6）：2771- 2793]和[S. Maset，SIAM J. Numer. Anal.（2015）53（6）：2794- 2821]。我们严格表明，作为一个边值问题需要一个适当的无限维边界周期性条件，以便进行这种分析的重新制定。在这方面，我们还强调了作为未知参数的周期的作用，这是至关重要的，因为它与时间的进程直接相关。最后，我们证明了有限元法是收敛的，而我们只限于评论这种方法的不可行性，就谱元法而言。
英文摘要：
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.
Periodic B-spline-Heaviside collocation for Fredholm integral equations with piecewise Hölder data
Institute of Mathematics and Computer Science, Moldova State University（摩尔多瓦国立大学数学与计算机科学研究所）；Department of Computer Science, Moldova State University（摩尔多瓦国立大学计算机科学系）
Physics-informed deep learning and compressive collocation for high-dimensional diffusion-reaction equations: practical existence theory and numerics
Department of Mathematics and Statistics（数学与统计学系）；Concordia University（康科迪亚大学）；Department of Scientific Computing（科学计算系）；Florida State University（佛罗里达州立大学）；Department of Physics & Astronomy（物理与天文学系）；University of Victoria（维多利亚大学）
