I have to simulate the behaviour of a magnetic system described by a generalised Landau Lifshitz Gilbert equation, which looks like:
dm/dt = k1*mxH + k2*mx(mxH) + k3*cos(w*t)*mx(mxv) + k4*cos(w*t)*mx(mx(mxv))
- m is a 3*1 vector
- the ki's are constant coefficients
- H is a vector depending on both m and t, i.e. H = H(m,t)
- v is a constant vector
- * stands for the usual product
- x stands for the vector product
The starting point is an equilibrium point (for t = 0, so that the cos are unity) and then I got very different results depending on the solver I used. My guess was that the equation is stiff but even with stiff solvers, the solution doesn't look like what I expect. I tried to reduce the step size as much as possible but the problem remains.
Here is a picture of the different solutions with the different solvers for one of the components of m.
The stiff solvers basically give a constant zero solution (not visible on the plot), but I would have expected some oscillations in any case. Do you have any idea what I could do to get a proper solution?