English

A note on the L1 discretization error for the Caputo derivative in H\"older spaces

Numerical Analysis 2024-11-19 v1 Numerical Analysis

Abstract

We establish uniform error bounds of the L1 discretization of the Caputo derivative of H\"older 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.

Keywords

Cite

@article{arxiv.2411.10833,
  title  = {A note on the L1 discretization error for the Caputo derivative in H\"older spaces},
  author = {Félix del Teso and Łukasz Płociniczak},
  journal= {arXiv preprint arXiv:2411.10833},
  year   = {2024}
}