We provide the convergence analysis for a sinc-Galerkin method to solve the fractional Dirichlet problem. This can be understood as a follow-up of an earlier article by the same authors, where the authors presented a sinc-function based method to solve fractional PDEs. While the original method was formulated as a collocation method, we show that the same method can be interpreted as a nonconforming Galerkin method, giving access to abstract error estimates. Optimal order of convergence is shown without any unrealistic regularity assumptions on the solution.

翻译：本文针对利用sinc-Galerkin方法求解分数阶Dirichlet问题的收敛性进行了分析。本研究可视为作者前期工作的延续——彼时已提出基于sinc函数的分数阶偏微分方程数值解法。虽然原始方法采用配置法形式，但本文证明该方法可等效为非协调Galerkin方法，从而为抽象误差估计提供了理论途径。在不依赖解的非现实正则性假设条件下，本文证明了最优收敛阶。