A note on the L1 discretization error for the Caputo derivative in Hölder spaces
arXiv:2411.10833 · doi:10.1016/j.aml.2024.109364
Abstract
We establish uniform error bounds of the L1 discretization of the Caputo derivative of Hölder continuous functions. The result can be understood as: error = (degree of smoothness - order of the derivative). We present an elementary proof and illustrate its optimality with numerical examples.