I'm testing a code to find periodic solutions of nonlinear structural vibrating systems by solving a global time-discretized periodic system of equations. I am using a forward Euler (first order explicit) approximation in velocities and accelerations. I find my solution, yet compared to a explicit time marching code, the solution exhibits an increased damping. I've validated the classic time marching signal with a bunch of different methods and they are consistent. From what I understand, forward Euler shouldn't have a numerical damping associated with it right?
How would I mathematically prove if a time discretization produces numerical damping or not?
As requested, to let the question get answered...
There's not much you can do if you're working with forward euler. Forward euler is the simplest possible explicit method, it's just a projection of the most fundamental finite difference approximation of the derivative. Step-size is your only free parameter. If your solution is periodic, however, then you might instead be able to re-scale the proble (say, reduce the period), then undo that scale change after solving