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Numerical simulation of time-fractional partial differential equations arising in fluid flows via reproducing Kernel method

Omar Abu Arqub (Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt, Jordan)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 16 July 2019

Issue publication date: 15 October 2020

Abstract

Purpose

The subject of the fractional calculus theory has gained considerable popularity and importance due to their attractive applications in widespread fields of physics and engineering. The purpose of this paper is to present results on the numerical simulation for time-fractional partial differential equations arising in transonic multiphase flows, which are described by the Tricomi and the Keldysh equations of Robin functions types.

Design/methodology/approach

Those resulting mathematical models are solved by using the reproducing kernel method, which provide appropriate solutions in term of infinite series formula. Convergence analysis, error estimations and error bounds under some hypotheses, which provide the theoretical basis of the proposed method are also discussed.

Findings

The dynamical properties of these numerical solutions are discussed and the profiles of several representative numerical solutions are illustrated. Finally, the prospects of the gained results and the method are discussed through academic validations.

Originality/value

In this paper and for the first time: the authors presented results on the numerical simulation for classes of time-fractional PDEs such as those found in the transonic multiphase flows. The authors applied the reproducing kernel method systematically for the numerical solutions of time-fractional Tricomi and Keldysh equations subject to Robin functions types.

Keywords

Acknowledgements

The author would like to express his gratitude to the unknown referees for carefully reading the paper and their helpful comments.

Citation

Abu Arqub, O. (2020), "Numerical simulation of time-fractional partial differential equations arising in fluid flows via reproducing Kernel method", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 30 No. 11, pp. 4711-4733. https://doi.org/10.1108/HFF-10-2017-0394

Publisher

:

Emerald Publishing Limited

Copyright © 2019, Emerald Publishing Limited