Solving system of Euler's equations using Runge –Kutta methods

• Published in: مجلة جامعة الانبار للعلوم الصرفة Vol. 17; no. 2; pp. 265 - 268
• Main Authors: Aseel Al_Ameely, Athraa Albukhuttar
• Format: Journal Article
• Language: English
• Published: University of Anbar 01.12.2023
• Subjects: approximate solution; rung- kutta method; systems of euler equations
• ISSN: 1991-8941; 2706-6703
• DOI: 10.37652/juaps.2023.181576

In this paper, linear systems with variable coefficients (Euler's equations) were solved using one of the numerical methods that are subject to initial conditions defined over a given period of time .The explicit Rung-Kutta method is the fastest and most common numerical method starting with an initial value, the Rung-Kutta second order and Rung-Kutta fourth order. Analytical solutions of systems (systems with variable coefficients and systems with constant coefficients) were compared with the results of approximate solutions of the numerical method (Rung-Kutta second order And fourth order) and find out the accuracy of the results obtained for this approximate method after applying the Rung-Kutta algorithms performed with the Matlab program and finding the ratio of relative error between the exact and approximate solutions of the numerical method used, as well as solving a number of linear systems of Euler's equations of the first order supporting your results.