On the Use of Approximate Numerical and Analytical Methods in Order to solve the Differential Equations that Describe Vibrations of the Mechanical Systems

Abstract

The paper makes a comparative study on the approximation errors of the solutions of the differential equations of second order using different numerical methods, a study which is assessed by the necessity of numerical solving of the non-linear differential equations that describe the vibrations of the mechanical systems. For every resulted analytical solution from a differential equation we can compare the approximation errors for movement, speed and acceleration using the Runge-Kutta and finite differences methods. Then, the smallest approximation errors of the numerical method will be compared to the approximation errors using a linearization method that the author published in a previous paper. In the end, we present conclusions and recommendations concerning the use of approximation numerical methods for the approximate solutions.