Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative

ÇELİK C., DUMAN M.

JOURNAL OF COMPUTATIONAL PHYSICS, cilt.231, sa.4, ss.1743-1750, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 231 Sayı: 4
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1016/j.jcp.2011.11.008
  • Dergi Adı: JOURNAL OF COMPUTATIONAL PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1743-1750
  • Anahtar Kelimeler: Riesz fractional derivative operator, Crank-Nicolson method, Fractional centered difference, NUMERICAL-METHODS, APPROXIMATION
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

We examine a numerical method to approximate to a fractional diffusion equation with the Riesz fractional derivative in a finite domain, which has second order accuracy in time and space level. In order to approximate the Riesz fractional derivative, we use the "fractional centered derivative" approach. We determine the error of the Riesz fractional derivative to the fractional centered difference. We apply the Crank-Nicolson method to a fractional diffusion equation which has the Riesz fractional derivative, and obtain that the method is unconditionally stable and convergent. Numerical results are given to demonstrate the accuracy of the Crank-Nicolson method for the fractional diffusion equation with using fractional centered difference approach. Crown Copyright (C) 2011 Published by Elsevier Inc. All rights reserved.