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A finite difference method on quasi-uniform grids for the fractional boundary-layer Blasius flow

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  • Jannelli, Alessandra

Abstract

In this paper, we propose a fractional formulation, in terms of the Caputo derivative, of the Blasius flow described by a non-linear two-point fractional boundary value problem on a semi-infinite interval. We develop a finite difference method on quasi-uniform grids, based on a suitable modification of the classical L1 approximation formula and show the consistency, the stability and the convergence. The numerical results confirm the theoretical ones. Comparisons with some recently proposed results are carried out to validate the accuracy of the obtained numerical results, and to show the efficiency and the reliability of the proposed numerical method.

Suggested Citation

  • Jannelli, Alessandra, 2024. "A finite difference method on quasi-uniform grids for the fractional boundary-layer Blasius flow," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 382-398.
    • Handle: RePEc:eee:matcom:v:215:y:2024:i:c:p:382-398
    DOI: 10.1016/j.matcom.2023.08.023
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    References listed on IDEAS

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    1. Garrappa, Roberto, 2015. "Trapezoidal methods for fractional differential equations: Theoretical and computational aspects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 110(C), pages 96-112.
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    Cited by:

    1. Alessandra Jannelli & Maria Paola Speciale, 2024. "Fractional Boundary Layer Flow: Lie Symmetry Analysis and Numerical Solution," Mathematics, MDPI, vol. 12(2), pages 1-10, January.

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