There has been a greater attempt to solve differential equations by numerical methods. In this paper, we will treat the problem of system of two equations of first and second orders by using Newton’s Interpolation and Aitken's Methods and we will compare the results with Some Numerical Methods as the method of Euler method, Euler Cauchy method (Modified Euler Method) and Range Kutta method.
 M. E. Islama and M. A. Akbarb, Stable wave solutions to the Landau-Ginzburg-Higgs equation and the modified equal width wave equation using the IBSEF method. Arab J. Basic Appl. Sci. 27 (2020) 270-278
 C.K. Faith, Solution of first order differential equation using numerical newton’s interpolation and Lagrange method. Int. J. Dev. Res. 8 (2018) 18973-18976
 N.D. Ide, Using Newton’s interpolation and Aitken’s method for solving first order differential equation. World Appl. Sci. J. 38 (2020) 191-194
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
SYNAT - “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.