Work

Preconditioning fractional spectral collocation

Year: 2015

Type: preprint

Abstract: Fractional spectral collocation (FSC) method based on fractional Lagrange interpolation has recently been proposed to solve fractional differential equations. Numerical experiments show that the linear systems in FSC become extremely ill-conditioned as the number of collocation points increases. By introducing suitable fractional Birkhoff interpolation problems, we present fractional integration preconditioning matrices for the ill-conditioned linear systems in FSC. The condition numbers of the resulting linear systems are independent of the number of collocation points. Numerical examples are given.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1510.05776

Author: Du, Kui

Institution: Xiamen University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Ministry of Education of the People's Republic of China, Fundamental Research Funds for the Central Universities

Awards: G3762157797, G6641349758, G6843442997, G8818789539

OpenAlex ID: W2203282810

Cites: 7

Cited by: 1

Related to: 10