A weighted finite difference method for the fractional diffusion equation based on the Riemann-Liouville derivative
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Publication:2513947
DOI10.1016/J.APNUM.2014.11.007zbMATH Open1326.65111arXiv1109.2345OpenAlexW2138935277MaRDI QIDQ2513947
Author name not available (Why is that?)
Publication date: 29 January 2015
Published in: (Search for Journal in Brave)
Abstract: A one dimensional fractional diffusion model with the Riemann-Liouville fractional derivative is studied. First, a second order discretization for this derivative is presented and then an unconditionally stable weighted average finite difference method is derived. The stability of this scheme is established by von Neumann analysis. Some numerical results are shown, which demonstrate the efficiency and convergence of the method. Additionally, some physical properties of this fractional diffusion system are simulated, which further confirm the effectiveness of our method.
Full work available at URL: https://arxiv.org/abs/1109.2345
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