There are several methods for the approximate solution of the swing equations such as: Euler's method
, semi-implicit Euler method (trapezoidal), collocation, Runge Kutta, shampine, Radeau, among many more.
In order to compare with the result obtained with Euler's Method, (9) can be changed into
cr] of the slope obtained by Xiao and Yang  with Euler's Method is (ignoring the cohesion between the neighboring rock slabs)
When only the top loading shown in Figure 1 is considered, the CBH of the slope can be solved with Euler's Method, namely, (1).
cr], and according to Euler's Method, we can obtain
With Euler's Method, the rock is assumed to be a perfect linear elastic body and it does not fail.
Euler's method is used for the numerical solution whith the Taylor's expansion in this form (Butcher, 2003):
Numerical solution is achieved by using standard Euler's method (Butcher, 2003):
Applying Euler's method
to this equation yields the difference equation
The purpose of this paper is to demonstrate the importance of Euler's method.
To justify Euler's method we need the following Test by Markov.
The same environment is then used to explore solutions to the differential equations using Euler's method