Galerkin method with trigonometric basis on stable numerical differentiation

Yidong Luo

Applied Mathematics and Computation, 2020, vol. 370, issue C

Abstract: This paper considers the p (p=1,2,3) order numerical differentiation on function y in (0, 2π). They are transformed into corresponding Fredholm integral equation of the first kind. Computational schemes with analytic solution formulas are designed using Galerkin method on trigonometric basis. Convergence and divergence are all analysed in Corollaries 5.1, 5.2, and a-priori error estimate is uniformly obtained in Theorem 6.1, 7.1, 7.2. Therefore, the algorithm achieves the optimal convergence rate O(δ2μ2μ+1)(μ=12or1) with periodic Sobolev source condition of order 2µp. Besides, we indicate a noise-independent a-priori parameter choice when the function y possesses the form of∑k=0p−1aktk+∑k=1N1bkcoskt+∑k=1N2cksinkt,bN1,cN2≠0,In particular, in numerical differentiations for functions above, good filtering effect (error approaches 0) is displayed with corresponding parameter choice. In addition, several numerical examples are given to show that even derivatives with discontinuity can be recovered well.

Keywords: Numerical differentiation; Galerkin method; Fourier expansion; Regularization (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S009630031930904X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:370:y:2020:i:c:s009630031930904x

DOI: 10.1016/j.amc.2019.124912

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().