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A high-order compact difference method for fractional sub-diffusion equations with variable coefficients and nonhomogeneous Neumann boundary conditions

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Abstract

In a recent paper, Ren and Liu proposed and analyzed a high-order compact finite difference method for a class of fractional sub-diffusion equations with variable coefficients and nonhomogeneous Neumann boundary conditions. In this paper, we point out some deficiencies and errors found in that paper and make the corresponding revisions.

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References

  • Alikhanov AA (2015) A new difference scheme for the time fractional diffusion equation. J Comput Phys 280:424–438

    Article  MathSciNet  Google Scholar 

  • Liao H, Mclean W, Zhang J (2019) A discrete grönwall inequality with application to numerical schemes for subdiffusion problems. arXiv:1803.09879v2

  • Ren L, Liu L (2018) Efficient compact finite difference method for variable coefficient fractional sub-diffusion equations with nonhomogeneous Neumann boundary conditions in conservative form. Comput Appl Math. https://doi.org/10.1007/s40314-018-0690-7

    Article  MathSciNet  Google Scholar 

  • Samarskii AA, Andreev VB (1976) Difference Methods for Elliptic Equations. Nauka, Moscow (in Russian)

  • Sun Z (2001) An unconditionally stable and \({\cal{O}}(\tau ^{2}+h^{4})\) order \(L_{\infty }\) convergent difference scheme for linear parabolic equations with variable coefficients. Numer Methods Part Differ Equ 17:619–631

    Article  Google Scholar 

  • Varga RS (2000) Matrix iterative analysis. Springer, Berlin

    Book  Google Scholar 

  • Vong S, Lyu P, Wang Z (2016) A compact difference scheme for fractional sub-diffusion equations with the spatially variable coefficient under Neumann boundary conditions. J Sci Comput 66:725–739

    Article  MathSciNet  Google Scholar 

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Acknowledgements

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

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Authors and Affiliations

  1. Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, School of Mathematical Sciences, East China Normal University, Shanghai, 200241, People’s Republic of China

    Yuan-Ming Wang

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  1. Yuan-Ming Wang
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Correspondence to Yuan-Ming Wang.

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Communicated by José Tenreiro Machado.

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This work was supported in part by Science and Technology Commission of Shanghai Municipality (STCSM) (No. 18dz2271000)

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Wang, YM. A high-order compact difference method for fractional sub-diffusion equations with variable coefficients and nonhomogeneous Neumann boundary conditions. Comp. Appl. Math. 39, 13 (2020). https://doi.org/10.1007/s40314-019-0992-4

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  • DOI: https://doi.org/10.1007/s40314-019-0992-4

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