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Engineering with Computers

, Volume 35, Issue 1, pp 87–100 | Cite as

Numerical solution of a time-fractional PDE in the electroanalytical chemistry by a local meshless method

  • Gholamreza Karamali
  • Mehdi DehghanEmail author
  • Mostafa Abbaszadeh
Original Article

Abstract

In the current manuscript, we consider a fractional partial integro-differential equation that has some applications in the electroanalytical chemistry. The fractional derivative is based on the Riemann–Liouville fractional integral. The current numerical investigation is based on the following procedures: at first, a difference scheme has been used to discrete the temporal direction, second, the local RBF-DQ method is employed to discrete the spatial direction, and finally, these procedures are combined to obtain a full-discrete scheme. For the constructed numerical technique, we prove the unconditional stability and also obtain an error bound. We employ some test problems to show the accuracy of the proposed technique. In addition, we compare the obtained numerical results using the present method with the existing methods in the literature.

Keywords

Fractional partial integro-differential equation RBF-DQ method Finite-difference scheme Stability analysis Convergence analysis Energy method 

Notes

Acknowledgements

The authors are grateful to the reviewers for carefully reading this paper and 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

  • Gholamreza Karamali
    • 1
  • Mehdi Dehghan
    • 2
    Email author
  • Mostafa Abbaszadeh
    • 2
  1. 1.Faculty of Basic SciencesShahid Sattari Aeronautical University of Sciences and TechnologyTehranIran
  2. 2.Department of Applied Mathematics, Faculty of Mathematics and Computer SciencesAmirkabir University of TechnologyTehranIran

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