Numerical Spline Algorithm for Solving Falkner–Skan Equation

Authors

  • Suliman Mahmoud
  • Hasan Khalifa
  • Mariam Wassouf

Abstract

This paper presents a numerical spline algorithm for the Falkner–Skan equation (FSE) over a semi-infinite interval. This algorithm is based on change of variable from interval  to [0,1], then the FSE is transformed into first initial value problem (IVP) and second IVP for improving convergence.  Spline polynomials with four collocation points are applied directly to the IVPs without their reducing to a system of first-order differential equations. The study shows that purposed algorithm is consistent and convergent with a global truncation error from order eighth. The efficacy of our algorithm is tested by solving the problems of Blasius, Pohlhausen, Homann and Hiemenz flows, and other special cases over various intervals, where the results of comparisons with other methods indicate the efficiency of our algorithm and enable it to provide solutions with high numerical accuracy.

 

Downloads

Published

2019-12-31

How to Cite

1.
Mahmoud S, Khalifa H, Wassouf M. Numerical Spline Algorithm for Solving Falkner–Skan Equation. TUJ-BA [Internet]. 2019Dec.31 [cited 2025Apr.6];41(6). Available from: https://journal.tishreen.edu.sy/index.php/bassnc/article/view/9365

Issue

Vol. 41 No. 6 (2019): Tishreen University Journal for Research and Scientific Studies - Basic Sciences Series

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

The authors retain the copyright and grant the right to publish in the magazine for the first time with the transfer of the commercial right to the Tishreen University Journal -Basic Sciences Series  

 Under a CC BY- NC-SA 04 license that allows others to share the work with of the work's authorship and initial publication in this journal. Authors can use a copy of their articles in their scientific activity, and on their scientific websites, provided that the place of publication is indicted in Tishreen University Journal -Basic Sciences Series .  The Readers have the right to send, print and subscribe to the initial version of the article, and the title of Tishreen University Journal -Basic Sciences Series   Publisher

 

journal uses a CC BY-NC-SA license which mean

You are free to:

  • Adapt — remix, transform, and build upon the material
  •  
  • The licensor cannot revoke these freedoms as long as you follow the license terms.

 

  • Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • NonCommercial — You may not use the material for commercial purposes.
  • ShareAlike — If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.
  • No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.