2022/12/22 by Harbir Antil, Patrick Dondl, Antil, Harbir +3 · 1 citation
Mathematics · Computer Science · #Differential Equations and Numerical Methods #Fractional Differential Equations Solutions #Advanced Mathematical Modeling in Engineering
paper · pdf · doi:10.48550/arxiv.2212.11581
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.