Preconditioning fractional spectral collocation

2015/10/20 by Kui Du, Du, Kui · 1 citation
Engineering · Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1510.05776

openalex publication_date 2015/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

Citations

• Preconditioning rectangular spectral collocation
• Well-Conditioned Fractional Collocation Methods Using Fractional Birkhoff Interpolation Basis

Cited by

• On well-conditioned spectral collocation and spectral methods by the integral reformulation

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