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Numerical investigation of the nonlinear modified anomalous diffusion process

  • O. Nikan
  • J. A. Tenreiro Machado
  • A. GolbabaiEmail author
  • T. Nikazad
Original paper
  • 52 Downloads

Abstract

The nonlinear modified anomalous sub-diffusion model characterizes processes that become less anomalous as time progresses by including a second fractional time derivative acting on the term of diffusion. This paper introduces a radial basis function-generated finite difference (RBF-FD) method for solving the governing problem. The Grünwald–Letnikov formula with first-order accuracy is implemented to discretize the problem in the time direction, and the spatial variable is discretized using the local RBF-FD method. The convergence and stability of the time discretization scheme are deduced in an appropriate Sobolev space. The data distribution pattern within the support domain is considered to have a constant number of points. The numerical results on regular and irregular domains show the efficiency and high accuracy of the method and confirm the theoretical prediction.

Keywords

Riemann–Liouville fractional derivative Modified anomalous sub-diffusion model RBF-FD Stability Convergence 

Mathematics Subject Classification

35R11 65M70 91G60 34K37 

Notes

Acknowledgements

The authors are deeply grateful to Associate Editor for managing the review process.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this article.

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of MathematicsIran University of Science and TechnologyNarmak, TehranIran
  2. 2.Department of Electrical Engineering, ISEP-Institute of EngineeringPolytechnic of PortoPortoPortugal

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