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

Hossein Pourbashash and Mahmood Khaksar-e Oshagh

Applied Mathematics and Computation, 2018, vol. 339, issue C, 144-152

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.

Keywords: Riemann–Liouville fractional derivative; RBF-FD method; Finite difference scheme; Stability analysis; Convergence analysis; Energy method (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:339:y:2018:i:c:p:144-152

DOI: 10.1016/j.amc.2018.06.043

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