A note on the L1 discretization error for the Caputo derivative in Hölder spaces

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2024-11-09 DOI:10.1016/j.aml.2024.109364

Félix del Teso , Łukasz Płociniczak

引用次数: 0

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.

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关于赫尔德空间中卡普托导数的 L1 离散误差的说明

我们建立了赫尔德连续函数卡普托导数 L1 离散化的均匀误差边界。其结果可理解为：误差 = 平滑度 - 导数阶数。我们给出了一个基本证明，并通过数值示例说明了其最优性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.