  In our previous work, numerical schemes for a simplified version of 3-wave
kinetic equations, in which only the simple forward-cascade terms of the
collision operators are kept, have been successfully designed, especially to
capture the long time dynamics of the equation given the multiple blow-up time
phenomenon. In this second work in the series, we propose numerical treatments
for the complete 3-wave kinetic equations, in which the complete, much more
complicated collision operators are fully considered based on a novel
conservative form of the equation. We then derive an implicit finite volume
scheme to solve the equation. The new discretization uses an adaptive
time-stepping method which allows for the simulations to be carried to very
long times. Our computed solutions are compared with previously derived
long-time asymptotic estimates for the decay rate of total energy of
time-dependent solutions of 3-wave kinetic equations and found to be in
excellent agreement.
