A fast and spectrally convergent algorithm for rational-order fractional integral and differential equations

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Title: A fast and spectrally convergent algorithm for rational-order fractional integral and differential equations
Authors: Hale, N
Olver, SS
Item Type: Journal Article
Abstract: A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for ordinary differential equations [27], and involves constructing two different bases, one for the domain of the operator and one for the range of the operator. The bases are constructed from direct sums of suitably weighted ultraspherical or Jacobi polynomial expansions, for which explicit representations of fractional integrals and derivatives are known, and are carefully chosen so that the resulting operators are banded or almost-banded. Geometric convergence is demonstrated for numerous model problems when the variable coefficients and right-hand side are sufficiently smooth.
Date of Acceptance: 23-Apr-2018
URI: http://hdl.handle.net/10044/1/59264
ISSN: 1064-8275
Publisher: Society for Industrial and Applied Mathematics
Journal / Book Title: SIAM Journal on Scientific Computing
Copyright Statement: This paper is embargoed until publication.
Keywords: 0102 Applied Mathematics
0103 Numerical And Computational Mathematics
0802 Computation Theory And Mathematics
Numerical & Computational Mathematics
Publication Status: Accepted
Embargo Date: publication subject to indefinite embargo
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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