Fractional spectral differentiation matrices based on Legendre approximation

Advances in Difference Equations

article

Ghorbani, Asghar¹  Baleanu, Dumitru² 

[1] Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad;Department of Mathematics, Cankaya University;Department of Medical Research, China Medical University;Institute of Space Sciences

关键词: Fractional spectral differentiation matrices;    Fractional calculus;    Legendre polynomials;    Numerical differentiation;   

DOI  :  10.1186/s13662-020-02590-4

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

A simple scheme is proposed for computing $N \times N$ spectral differentiation matrices of fractional order α for the case of Legendre approximation. The algorithm derived here is based upon a homogeneous three-term recurrence relation and is numerically stable. The matrices are then applied to numerically differentiate.

【 授权许可】

CC BY