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Journal of Scientific Computing

, Volume 79, Issue 1, pp 227–248 | Cite as

A Gauss–Jacobi Kernel Compression Scheme for Fractional Differential Equations

  • Daniel BaffetEmail author
Article

Abstract

A scheme for approximating the kernel w of the fractional \(\alpha \)-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 \([\delta ,T]\), with \(0<\delta \), 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 \(\alpha \in (0,1)\), and that J is bounded for \(\alpha \in (0,1)\), \(T>0\), and \(\delta \in (0,T)\).

Keywords

Fractional differential equations Volterra equations Gaussian quadratures Kernel compression Local schemes 

Notes

Acknowledgements

The author declares that he has no conflict of interests.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of BaselBaselSwitzerland

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