Efficient high order algorithms for fractional integrals and fractional differential equations

Lehel Banjai, M. Lopez-Fernandez

Research output: Contribution to journalArticle

9 Citations (Scopus)
15 Downloads (Pure)

Abstract

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)1-29
Number of pages29
JournalNumerische Mathematik
Early online date24 Oct 2018
DOIs
Publication statusE-pub ahead of print - 24 Oct 2018

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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