The BDF3/EP3 Scheme for MBE with No Slope Selection is Stable

We consider the classical molecular beam epitaxy (MBE) model with logarithmic type potential known as no-slope-selection. employ a third order backward differentiation (BDF3) in time implicit treatment of surface diffusion term. The nonlinear term is approximated by explicit extrapolation (EP3) formula. exhibit mild step constraints under which modified energy dissipation law holds. break second Dahlquist barrier and develop new theoretical framework to prove unconditional uniform boundedness no size restrictions on step. This first result for BDF methods applied MBE models without introducing any stabilization or fictitious variable. analysis can be generalized restrictive class phase field whose nonlinearity has bounded derivatives. A novel also established error high methods.