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A convergent exponential B-spline collocation method for a time-fractional telegraph equation

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Abstract

This work aims to develop and analyze a numerical method for solving a time-fractional telegraph equation of Caputo type. The method is constructed using a finite difference method for the time discretization and exponential B-spline functions for the space discretization. The unique solvability is well demonstrated. The convergence of the method is discussed in detail and the proposed method is shown to be convergent with the convergence order \(O(h^{2},\Delta t)\), where h and \(\Delta t\) represent mesh sizes in the space and time directions, respectively. The proposed numerical method is employed on two test problems, and their results have manifested the eminence and validity of our approach.

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Acknowledgements

The first author gratefully acknowledge the support of University Grant Commission, India, for research fellowship. The authors would like to express great appreciation to the editor and anonymous reviewers for their valuable comments and constructive suggestions, which have helped to improve the quality and presentation of this paper.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, Uttar Pradesh, India

    Anshima Singh & Sunil Kumar

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  1. Anshima Singh
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  2. Sunil Kumar
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Correspondence to Sunil Kumar.

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Communicated by Kassem Mustapha.

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Singh, A., Kumar, S. A convergent exponential B-spline collocation method for a time-fractional telegraph equation. Comp. Appl. Math. 42, 79 (2023). https://doi.org/10.1007/s40314-023-02213-0

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