arXiv Computer Science
arXiv Computer Science
Preprint
2 years ago

A Higher Order Resolvent-positive Finite Difference Approximation for Fractional Derivatives. (arXiv:2112.08529v2 [math.NA] UPDATED)

Boris Baeumer, Mihály Kovács, Matthew Parry
We develop a finite difference approximation of order for the -fractional derivative. The weights of the approximation scheme have the same rate-matrix type properties as the popular Gr\"unwald scheme. In particular, approximate solutions to fractional diffusion equations preserve positivity. Furthermore, for the approximation of the solution to the skewed fractional heat equation on a bounded domain the new approximation scheme keeps its order whereas the order of the Gr\"unwald scheme reduces to order , contradicting the convergence rate results by Meerschaert and Tadjeran.

Publisher URL: https://arxiv.org/abs/2112.08529

DOI: arXiv:2112.08529v2

You might also like
Discover & Discuss Important Research

Keeping up-to-date with research can feel impossible, with papers being published faster than you'll ever be able to read them. That's where Researcher comes in: we're simplifying discovery and making important discussions happen. With over 19,000 sources, including peer-reviewed journals, preprints, blogs, universities, podcasts and Live events across 10 research areas, you'll never miss what's important to you. It's like social media, but better. Oh, and we should mention - it's free.

  • Download from Google Play
  • Download from App Store
  • Download from AppInChina

Researcher displays publicly available abstracts and doesn’t host any full article content. If the content is open access, we will direct clicks from the abstracts to the publisher website and display the PDF copy on our platform. Clicks to view the full text will be directed to the publisher website, where only users with subscriptions or access through their institution are able to view the full article.