Document Type : Research Paper
Authors
1 Department of Mathematics, College of Education for Girls, University of Al-Kufa, Najaf – Iraq
2 Department of Mathematics, College of Education for Girls, University of Al-Kufa, Najaf , Iraq;
Abstract
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.
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