A Jacobi spectral method for calculating fractional derivative based on mollification regularization

被引：2
|
作者：
Zhang, Wen [1 ]
Wu, Changxing [1 ]
Ruan, Zhousheng [1 ]
Qiu, Shufang [1 ,2 ]
机构：
[1] East China Univ Technol, Sch Sci, Nanchang 330013, Jiangxi, Peoples R China
[2] Guangzhou Maritime Univ, Dept Basic Courses, Guangzhou 510725, Guangdong, Peoples R China
来源：
ASYMPTOTIC ANALYSIS | 2024年 / 136卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Fractional derivative; Jacobi collocation; mollification; Gaussian quadrature; APPROXIMATIONS; INTERPOLATION; EQUATION;
D O I：
10.3233/ASY-231869
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we construct a Jacobi spectral collocation scheme to approximate the Caputo fractional derivative based on Jacobi-Gauss quadrature. The convergence analysis is provided in anisotropic Jacobi-weighted Sobolev spaces. Furthermore, the convergence rate is presented for solving Caputo fractional derivative with noisy data by invoking the mollification regularization method. Lastly, numerical examples illustrate the effectiveness and stability of the proposed method.
引用
收藏
页码：61 / 77
页数：17
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