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The local discontinuous Galerkin method for 2D nonlinear time-fractional advection–diffusion equations

  • Jafar Eshaghi
  • Saeed Kazem
  • Hojjatollah Adibi
Original Article
  • 16 Downloads

Abstract

This paper presents a numerical solution of time-fractional nonlinear advection–diffusion equations (TFADEs) based on the local discontinuous Galerkin method. The trapezoidal quadrature scheme (TQS) for the fractional order part of TFADEs is investigated. In TQS, the fractional derivative is replaced by the Volterra integral equation which is computed by the trapezoidal quadrature formula. Then the local discontinuous Galerkin method has been applied for space-discretization in this scheme. Additionally, the stability and convergence analysis of the proposed method has been discussed. Finally some test problems have been investigated to confirm the validity and convergence of the proposed method.

Keywords

Time-fractional advection–diffusion equations Discontinuous Galerkin method Local discontinuous Galerkin method Caputo derivative Stability and convergence analysis 

Mathematics Subject Classification

45D05 45G05 41A30 

Notes

Acknowledgements

The authors are grateful to the reviewers for their comments and suggestions which have improved the paper.

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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Applied Mathematics, Faculty of Mathematics and Computer ScienceAmirkabir University of TechnologyTehranIran

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