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Local RBF-FD technique for solving the two-dimensional modified anomalous sub-diffusion equation

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  • Pourbashash, Hossein
  • Khaksar-e Oshagh, Mahmood

Abstract

The main aim of this paper is to propose an efficient and suitable numerical procedure based on the local meshless collocation method for solving the two-dimensional modified anomalous sub-diffusion equation. The fractional derivative is based on the Riemann–Liouville fractional integral. Firstly, a finite difference scheme with O(τ) has been employed to discrete the time variable and also the local radial basis-finite difference (LRBF-FD) method is used to discrete the spatial direction. For the presented numerical technique, we prove the unconditional stability and also obtain an error bound. We employ a test problem to show the accuracy of the proposed technique. Also, we solve the mentioned model on irregular domain to show the efficincy of the developed technique.

Suggested Citation

  • Pourbashash, Hossein & Khaksar-e Oshagh, Mahmood, 2018. "Local RBF-FD technique for solving the two-dimensional modified anomalous sub-diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 144-152.
    • Handle: RePEc:eee:apmaco:v:339:y:2018:i:c:p:144-152
    DOI: 10.1016/j.amc.2018.06.043
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