We have not built energy constraints into our algorithms to solve differential equations. Yet conservation of energy is not only a basic principle in Physics but often it is a very useful tool. For an oscillating system without external driving forces and friction the sum of the kinetic energy and the potential energy has to be constant.
We can use this to test the accuracy of our solution. If the energy doesn't stay constant for all times then we have to change the step size of our algorithm or even use a different method to solve our problem.