I'm working on a time integration scheme for my research. As a result, I have come across an interesting phenomenon. Somehow, the total energy of the scheme oscillates. At any given time the total energy of the system could be increasing or decreasing but does so in a oscillatory fashion. Interestingly enough, for what I'm modeling, this integration scheme works great. I'm curious if there is a way to prove whether the energy of this scheme is stable throughout the time history.
FYI, I'm a Ph.D. student in structural engineering. So, this topic is a little out of my field. I'm just curious if the scheme is stable or not, and if it can be proven. Are their other time integration schemes that don't satisfy the conservation of energy but remain stable? Thanks.