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

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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.

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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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Authors and Affiliations

  1. Faculty of Basic Sciences, Shahid Sattari Aeronautical University of Sciences and Technology, South Mehrabad, Tehran, Iran

    Gholamreza Karamali

  2. Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, 15914, Iran

    Mehdi Dehghan & Mostafa Abbaszadeh

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  1. Gholamreza Karamali
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  2. Mehdi Dehghan
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  3. Mostafa Abbaszadeh
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Correspondence to Mehdi Dehghan.

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Karamali, G., Dehghan, M. & Abbaszadeh, M. Numerical solution of a time-fractional PDE in the electroanalytical chemistry by a local meshless method. Engineering with Computers 35, 87–100 (2019). https://doi.org/10.1007/s00366-018-0585-7

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