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An Efficient Numerical Method for Fractional Advection–Diffusion–Reaction Problem with RLC Fractional Derivative

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Abstract

In this paper, we consider a two-point boundary-value problem with a Riemann–Liouville–Caputo fractional derivative of order \(\alpha \in (1,2)\). We solve this boundary-value problem in a sequence of processes, first using the shooting technique based on the secant iterative method, we convert the boundary-value problem into an initial-value problem, then the initial-value problem is transformed into an equivalent Volterra integral equation with weakly singular kernel. Finally, we find the approximate solution of the resultant equation by using a discretization scheme on a uniform mesh. The method’s convergence analysis has been thoroughly established, and it demonstrates that the scheme is first-order convergent. To show the effectiveness of the suggested approach, numerical results are provided.

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Acknowledgements

The authors thank the referees for their insightful comments and recommendations, which helped to make the article better. The first author would like to thank IIT Guwahati for their assistance with the fellowship and facilities during his research.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati, 781039, India

    Sandip Maji & Srinivasan Natesan

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  1. Sandip Maji
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  2. Srinivasan Natesan
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Contributions

S.N proposed the research problem and methods to solve the equation. S.M. implemented the scheme and derived the error estimates and implemented the scheme in the computer. Both of us reviewed the manuscript.

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Correspondence to Srinivasan Natesan.

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Maji, S., Natesan, S. An Efficient Numerical Method for Fractional Advection–Diffusion–Reaction Problem with RLC Fractional Derivative. Mediterr. J. Math. 20, 297 (2023). https://doi.org/10.1007/s00009-023-02499-8

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  • DOI: https://doi.org/10.1007/s00009-023-02499-8

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