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A numerical technique based on multiplicative integration strategy for fractional Darboux problem

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Abstract

In this paper, a numerical strategy is introduced for solving a class of linear fractional-order Darboux problem that includes the Caputo derivative. The presented strategy is grounded on the Newton-Cotes quadrature rule and is established by implementing Lagrange interpolation polynomial. A formula is developed to evaluate the two-dimensional fractional integrals by using the multiplicative integration strategy. Then, this formula is employed to derive a scheme for solving a class of fractional-order Darboux problem. The accuracy and efficiency of all the presented schemes are illustrated through numerical experiments. Furthermore, the estimation of the upper bounds of error in the numerical approximation for the proposed multiplicative integration strategy is established.

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No data was used for the research described in the article.

Code availability

The computational codes are available from the corresponding author on request.

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  1. Both authors have contributed equally.

Authors and Affiliations

  1. Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan

    Amna Bibi & Mujeeb ur Rehman

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  1. Amna Bibi
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Bibi, A., ur Rehman, M. A numerical technique based on multiplicative integration strategy for fractional Darboux problem. Numer Algor 97, 617–643 (2024). https://doi.org/10.1007/s11075-023-01718-3

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