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arXiv · 2504.07391

High-order discretization errors for the Caputo derivative in H\"{o}lder spaces

Xiangyi Peng·Lisen Ding·Dongling Wang
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Abstract

Building upon the recent work of Teso and Plociniczak (2025) regarding L1 discretization errors for the Caputo derivative in H\"{o}lder spaces, this study extends the analysis to higher-order discretization errors within the same functional framework. We first investigate truncation errors for the L2 and L1-2 methods, which approximate the Caputo derivative via piecewise quadratic interpolation. Then we generalize the results to arbitrary high-order discretization. Theoretical analyses reveal a unified error structure across all schemes: the convergence order equals the difference between the smoothness degree of the function space and the fractional derivative order, i.e., order of error = degree of smoothness - order of the derivative. Numerical experiments validate these theoretical findings.

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Xiangyi Peng, Lisen Ding, Dongling Wang. 2025-04-10. High-order discretization errors for the Caputo derivative in H\"{o}lder spaces. https://arxiv.org/abs/2504.07391

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