Numerical Caputo Differentiation by Radial Basis Functions

被引：7

作者：

Li, Ming ^{[1
]}

Wang, Yujiao ^{[1
]}

Ling, Leevan ^{[2
]}

机构：

[1] Taiyuan Univ Technol, Dept Math, Taiyuan, Peoples R China

[2] Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2015年 / 62卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Fractional derivatives; Inverse problem; Convergence analysis; Noisy data; Regularization; FRACTIONAL DIFFUSION EQUATION; SPECTRAL METHOD; NOISY DATA; DERIVATIVES; REGULARIZATION;

D O I：

10.1007/s10915-014-9857-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Previously, based on the method of (radial powers) radial basis functions, we proposed a procedure for approximating derivative values from one-dimensional scattered noisy data. In this work, we show that the same approach also allows us to approximate the values of (Caputo) fractional derivatives (for orders between 0 and 1). With either an a priori or a posteriori strategy of choosing the regularization parameter, our convergence analysis shows that the approximated fractional derivative values converge at the same rate as in the case of integer order 1.

引用

页码：300 / 315

页数：16

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