We present a second order accurate in time numerical scheme for curve shortening flow in the plane that is unconditionally monotone. It is a variant of threshold dynamics, a class of algorithms in the spirit of the level set method that represent interfaces implicitly. The novelty is monotonicity: it is possible to preserve the comparison principle of the exact evolution while achieving second order in time consistency. As a consequence of monotonicity, convergence to the viscosity solution of curve shortening is ensured by existing theory.

翻译：我们提出了一个精确的第二顺序时间数字计划,以缩短平面的曲线流速,这是无条件的单质。它是临界动态的变体,一种符合隐含代表界面的定级方法精神的算法。新颖的是一种单一性:有可能保留精确演变的比较原则,同时实现时间的第二顺序。由于单质性,现有理论确保了与曲线缩短的粘度解决方案的趋同。