Numerical differentiation of the piecewise smooth function by using Fourier extension method

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI:10.1016/j.apnum.2024.09.026

Zhenyu Zhao , Kai Yu , Xianzheng Jia , Zhihong Dou

引用次数: 0

Abstract

Numerical differentiation of the piecewise smooth function is considered in this paper. To avoid the large error of numerical differentiation that may occur near potential non-smooth points, we identify the discontinuity points of the first or second derivative of the function. Then we divide the domain of the function into several sub-domains. For each sub-domain, the approximation is constructed by Fourier extension, and the global approximation of the piecewise smooth function is formed by superposition to improve accuracy. Some numerical experiments are conducted to further verify the efficacy of the method.

查看原文本刊更多论文

用傅里叶扩展法求分段光滑函数的数值微分

本文研究了分段光滑函数的数值微分问题。为了避免在潜在的非光滑点附近可能出现的较大数值微分误差，我们识别了函数的一阶或二阶导数的不连续点。然后将函数的定义域划分为若干子定义域。对于每个子域，通过傅里叶扩展构造近似，并通过叠加形成分段光滑函数的全局近似，提高精度。通过数值实验进一步验证了该方法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.