Optimal Fractional Integration Preconditioning and Error Analysis of Fractional Collocation Method Using Nodal Generalized Jacobi Functions

• Main Authors: Huang, Can, Jiao, Yujian, Wang, Li-Lian, Zhang, Zhimin
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2017
• Subjects: Fractional Differential Equations; Riemann–Liouville Fractional Derivative
• Online Access: https://hdl.handle.net/10356/83949; http://hdl.handle.net/10220/42900
• Institution: Nanyang Technological University

In this paper, a nonpolynomial-based spectral collocation method and its well-conditioned variant are proposed and analyzed. First, we develop fractional differentiation matrices of nodal Jacobi polyfractonomials [M. Zayernouri and G. E. Karniadakis, J. Comput. Phys., 252 (2013), pp. 495--517] and g...