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：我们为Sinc-Galerkin解决分数dirichlet问题的方法提供了趋同分析。这可以理解为同一作者对早先的一篇文章的后续行动,在文章中,作者提出了一种基于sinc-职能的方法来解决分数的PDEs。虽然最初的方法是作为一种合用方法拟订的,但我们表明,同样的方法可以被解释为一种不符合Galerkin方法,可以使用抽象的误差估计。最佳的趋同顺序在解决方案上没有任何不切实际的规律性假设。