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A Gauss-Jacobi Kernel Compression Scheme for Fractional Differential Equations

Baffet, Daniel Henri. (2018) A Gauss-Jacobi Kernel Compression Scheme for Fractional Differential Equations. Journal of scientific computing, 79. pp. 227-248.

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Official URL: https://edoc.unibas.ch/75293/

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Abstract

A scheme for approximating the kernel w of the fractional α-integral by a linear combination of exponentials is proposed and studied. The scheme is based on the application of a composite Gauss–Jacobi quadrature rule to an integral representation of w. This results in an approximation of w in an interval [δ,T], with 0<δ, which converges rapidly in the number J of quadrature nodes associated with each interval of the composite rule. Using error analysis for Gauss–Jacobi quadratures for analytic functions, an estimate of the relative pointwise error is obtained. The estimate shows that the number of terms required for the approximation to satisfy a prescribed error tolerance is bounded for all α∈(0,1), and that J is bounded for α∈(0,1), T>0, and δ∈(0,T).
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Numerik (Grote)
UniBasel Contributors:Baffet, Daniel Henri
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Springer
ISSN:0885-7474
e-ISSN:1573-7691
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:25 Jun 2020 14:18
Deposited On:24 Jun 2020 15:42

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