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Numerical study of the boundary layer problem over a flat plate by orthogonal cubic spline basis functions

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Abstract

In this paper, the laminar boundary layer flow over a flat plate, governed by the Prandtl equations, has been studied numerically. The problem is a dimensionless third-order system of nonlinear ordinary differential equations which arises in boundary layer flow. This system is solved using an orthogonal basis for the space of cubic splines (O-splines), as an approximation tool. Some new properties of O-splines have been explored. Also, more accurate values for the initial value of the second derivative of the Falkner–Skan equation are obtained as an initial value inverse problem. Using the new initial values, the problem becomes a first-order system of ordinary differential equations which is solved by the RK45 method and the results are compared with the presented method.

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: All data included in this manuscript are available upon request by contacting with the corresponding author.]

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, 41938, Iran

    Javad Alavi & Hossein Aminikhah

  2. Center of Excellence for Mathematical Modelling, Optimization and Combinational Computing (MMOCC), University of Guilan, P.O. Box 1914, Rasht, 41938, Iran

    Hossein Aminikhah

Authors
  1. Javad Alavi
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  2. Hossein Aminikhah
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Correspondence to Hossein Aminikhah.

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Alavi, J., Aminikhah, H. Numerical study of the boundary layer problem over a flat plate by orthogonal cubic spline basis functions. Eur. Phys. J. Plus 136, 780 (2021). https://doi.org/10.1140/epjp/s13360-021-01788-z

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  • DOI: https://doi.org/10.1140/epjp/s13360-021-01788-z

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