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

翻译：我们考虑了古典分子束缩数模型(MBE),其对数类型潜力被称为无斜体选择;我们采用第三顺序后向差异(BDF3),及时对表面扩散术语进行隐含处理;非线性术语近似于第三顺序直线外推法(EP3)公式;我们展示了修改的能量消散法所遵循的温和时间步骤限制;我们打破了第二个达尔奎斯特屏障,并开发了新的理论框架,以证明无条件的统一能源界限,对时间步骤没有尺寸限制;这是在不引入任何稳定条件或虚构变量的情况下对MBE模型应用第三顺序BDF方法的第一个无条件结果;我们还为高顺序方法的错误分析建立了一个新的理论框架。