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Spectral collocation method for a class of fractional diffusion differential equations with nonsmooth solutions
Author(s) -
Wang Junjie,
Xiao Aiguo,
Bu Weiping
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6143
Subject(s) - mathematics , collocation method , spectral method , orthogonal collocation , collocation (remote sensing) , gauss , fractional calculus , mathematical analysis , gravitational singularity , convergence (economics) , basis (linear algebra) , polynomial , differential equation , ordinary differential equation , geometry , physics , remote sensing , quantum mechanics , geology , economic growth , economics
In this paper, we develop spectral collocation method for a class of fractional diffusion differential equations. Since the solutions of these fractional differential equations usually exhibit singularities at the end‐points, it can not be well approximated by classical polynomial basis functions. We first give nonclassical interpolants based on the associated Jacobi‐Gauss points and obtain the corresponding fractional differentiation matrices. Second, we prove the convergence for the developed spectral collocation method. Finally, several numerical examples are considered to demonstrate the validity and applicability of the developed basis functions.