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A class of moving Kriging interpolation-based DQ methods to simulate multi-dimensional space Galilei invariant fractional advection-diffusion equation

Abstract

The current work concerns to develop a new local meshless procedure to simulate the one-, two- and three-dimensional space Galilei invariant fractional advection-diffusion (GI-FAD) equations. The fractional derivative is discretized by a second-order finite difference formula. The unconditional stability and rate of convergence of the time-discrete scheme are analytically studied. Then, we employ the shape functions of moving Kriging interpolation for the differential quadrature (DQ) method. According to this combination, we can derive a new local meshless technique. At the end, some examples are solved to confirm the theoretical results and efficiency of the proposed meshless method.

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Acknowledgements

We would like to appreciate reviewers for their beneficial comments and suggestions that have improved our paper.

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Correspondence to Mostafa Abbaszadeh.

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Abbaszadeh, M., Dehghan, M. A class of moving Kriging interpolation-based DQ methods to simulate multi-dimensional space Galilei invariant fractional advection-diffusion equation. Numer Algor (2021). https://doi.org/10.1007/s11075-021-01188-5

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Keywords

  • Local meshless technique
  • Finite difference method
  • Unconditional stability
  • Differential quadrature (DQ) method
  • Fractional advection-diffusion equation

Mathematics Subject Classification (2010)

  • 65L60