Stability of results and time step ?

mnasri chokri

I am simulating equations in spectral variables , the general form of equations is d/dt+2.v.k^2)E(k,t)=T(k,t), the function T(k,t) contains linear and non-linear terms. I have problems with stability, I would like to know which terms may have influence on it, the time step for exemple , or k_min, k_max, k_pic(initial spectrum),the caractristic time, ...

thanks in advance.