https://doi.org/10.1140/epjs/s11734-025-01810-w
Regular Article
Approximation technique for transonic flows and weak shock reflection fractional models: collocation-based scale-3 Haar wavelet approach
1
Institute of Numerical Sciences, Kohat University of Science and Technology, 26000, Kohat, KP, Pakistan
2
Department of Basic Sciences, School of Electrical Engineering & Information Technology, German Jordanian University, 11180, Amman, Jordan
3
Department of Mathematics, College of Science, Taif University, 11099, 21944, Taif, Saudi Arabia
4
Department of Mathematics, College of Science, University of Ha’il, 2440, Ha’il, Saudi Arabia
Received:
19
February
2025
Accepted:
16
July
2025
Published online:
28
July
2025
Transonic flows and weak shock reflection can be modeled by Tricomi- and Keldysh-like equations. This paper aims to propose an efficient and reliable numerical technique employing scale-3 Haar wavelet along with numerical quadrature formula to study the dynamics of Tricomi- and Keldysh-like fractional problems. In this technique, the fractional Caputo temporal derivative is reinstated by the numerical quadrature formula. Then, the scale-3 Haar wavelet bases are encountered to estimate the solution and spatial derivatives. Following these steps the problem reduces to the system of linear algebraic equations. Solving the system leads to refine the solution and derivatives. Some benchmark illustrative numerical experiment are conducted to clarify the robustness of the suggest algorithm. Moreover, the computational stability is presented and linked with the absolute maximum eigenvalue (spectral radius) of the amplification matrix. The obtained results are compared with other existing numerical methods for validation. The accuracy is further elaborated by computing 
and 
error measures. Numerical simulations show that the outcomes of the proposed technique are promising
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
