It seems the only difference is the order to update $u$ and $v$?
zshearer
In response to the first question, it's when the total energy of the system decreases in a way not modeled by the system. Using the pendulum example, the pendulum will decrease in speed over time with backward euler, and eventually come to rest at 0, which is not the expected behavior of a frictionless system with no air resistance.
What is numerical damping?
Also, just to make sure I understand the difference between Forward Euler and Symplectic Euler.
$$ \ddot{u} = \Delta u $$
$$ u_{k+1} = u_k + \tau v_{k} \\ v_{k+1} = v_k + \tau \Delta u_k $$
$$ v_{k+1} = v_k + \tau \Delta u_k \\ u_{k+1} = u_k + \tau v_{k+1} $$
It seems the only difference is the order to update $u$ and $v$?
In response to the first question, it's when the total energy of the system decreases in a way not modeled by the system. Using the pendulum example, the pendulum will decrease in speed over time with backward euler, and eventually come to rest at 0, which is not the expected behavior of a frictionless system with no air resistance.
For the second question: you're correct.