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.

中文翻译：

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无斜率选择的MBE的BDF3/EP3方案是稳定的

我们考虑具有对数型势的经典分子束外延 (MBE) 模型，称为无斜率选择。我们及时采用三阶向后微分 (BDF3)，并对表面扩散项进行隐式处理。非线性项由三阶显式外推 (EP3) 公式近似。我们表现​​出温和的时间步长约束，在该约束下，修改后的能量耗散定律成立。我们打破了第二个 Dahlquist 障碍并开发了一个新的理论框架来证明无条件均匀能量有界，对时间步长没有大小限制。这是应用于 MBE 模型的三阶 BDF 方法的第一个无条件结果，而没有引入任何稳定项或虚拟变量。还为高阶方法的误差分析建立了一个新的理论框架。