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DOI 10.34229/KCA2522-9664.26.3.8
UDC 519.615:533.6.011.5

P.I. Stetsyuk
V.M. Glushkov Institute of Cybernetics, National Academy of Sciences
of Ukraine, Kyiv, Ukraine,stetsyukp@gmail.com

O.M. Khomiak
V.M. Glushkov Institute of Cybernetics, National Academy of Sciences
of Ukraine, Kyiv, Ukraine,khomiak.olha@gmail.com

M.M. Mitrakhovych
Ivchenko-Progress ZMKB, Zaporizhzhia, Ukraine,
mmma777@gmail.com

A.O Khorokhordin
Ivchenko-Progress ZMKB, Zaporizhzhia, Ukraine,
artem.khd@i.ua


JUSTIFICATION OF THE METHOD FOR SOLVING THE TRANSCENDENT
RANKINE–HUGONIO EQUATION

Abstract. Methods for solving the transcendental Rankine–Hugoniot equation for determining the characteristics of a supersonic and hypersonic input device are investigated. Lower and upper bounds for the shock wave angle are established, which determine the interval of existence of a unique solution to the Rankine–Hugoniot equation. The convergence rates of the dichotomy method, the chord method, the secant method, and the Newton method are compared, and it is established that the secant and Newton methods are the most effective in terms of the number of iterations. The experimental results show that preference should be given to the secant method, the iteration complexity of which is less than the iterations of the Newton method.

Keywords: input device, deflection angle, shock wave angle, Mach number, adiabatic index, methods for finding the root of the transcendental equation.


full text

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