Efficient high order algorithms for fractional integrals and fractional differential equations

Lehel Banjai*, M. Lopez-Fernandez

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Citations (Scopus)
71 Downloads (Pure)


We propose an efficient algorithm for the approximation of fractional integrals by using Runge–Kutta based convolution quadrature. The algorithm is based on a novel integral representation of the convolution weights and a special quadrature for it. The resulting method is easy to implement, allows for high order, relies on rigorous error estimates and its performance in terms of memory and computational cost is among the best to date. Several numerical results illustrate the method and we describe how to apply the new algorithm to solve fractional diffusion equations. For a class of fractional diffusion equations we give the error analysis of the full space-time discretization obtained by coupling the FEM method in space with Runge–Kutta based convolution quadrature in time.

Original languageEnglish
Pages (from-to)289–317
Number of pages29
JournalNumerische Mathematik
Early online date24 Oct 2018
Publication statusPublished - 13 Feb 2019

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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