A high-order compact difference method for time fractional Fokker–Planck equations with variable coefficients

Abstract

A high-order compact finite difference method is proposed for time fractional Fokker–Planck equations with variable convection coefficients. This method leads to a very simple and yet efficient compact finite difference scheme with high-order accuracy. It is also very convenient for us to give the corresponding analysis of stability and convergence using a discrete energy method. The proposed method is unconditionally stable and convergent with the convergence order \(\mathcal{O}(\tau ^{2}+h^{4})\), where \(\tau \) and h are the step sizes in time and space, respectively. Thus, it improves the convergence order of some recently developed methods. Numerical results confirm the theoretical analysis and demonstrate the high efficiency of this novel method.

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Acknowledgements

The authors would like to thank the referees for their valuable comments and suggestions which improved the presentation of this paper.

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Correspondence to Lei Ren.

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This work was supported in part by National Natural Science Foundation of China (No. 11401363)

Communicated by José Tenreiro Machado.

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Ren, L., Liu, L. A high-order compact difference method for time fractional Fokker–Planck equations with variable coefficients. Comp. Appl. Math. 38, 101 (2019). https://doi.org/10.1007/s40314-019-0865-x

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Keywords

  • Fractional Fokker–Planck equation
  • Compact finite difference method
  • Stability
  • High-order convergence
  • Energy method

Mathematics Subject Classification

  • 65M06
  • 65M12
  • 65M15
  • 35R11