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Numerical investigation of the nonlinear modified anomalous diffusion process

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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.

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Acknowledgements

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Authors and Affiliations

  1. School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran

    O. Nikan, A. Golbabai & T. Nikazad

  2. Department of Electrical Engineering, ISEP-Institute of Engineering, Polytechnic of Porto, Porto, Portugal

    J. A. Tenreiro Machado

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  1. O. Nikan
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Nikan, O., Tenreiro Machado, J.A., Golbabai, A. et al. Numerical investigation of the nonlinear modified anomalous diffusion process. Nonlinear Dyn 97, 2757–2775 (2019). https://doi.org/10.1007/s11071-019-05160-w

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