变步长无条件稳定的Dahlquist，Liniger和Nevanlinna方法的重构
Refactorization of a variable step, unconditionally stable method of Dahlquist, Liniger and Nevanlinna
摘要：
Dahlquist、Liniger和Nevanlinna提出的单支两步时间步长格式在复杂的、刚性的数值模拟中具有明显的优势：变时间步长的无条件$G$稳定性和二阶精度。然而，由于直接执行的复杂性，该机制一直未得到充分利用。本文证明了这种方法与加了前后运算步骤的后向欧拉法是等价的。这种重构简化了复杂的、可能是遗留代码的实现。我们开发的实现降低了复杂性，包括认知复杂性，并提高了一阶方法和恒定时间步长二阶方法的精度。
英文摘要：
The one-leg, two-step time-stepping scheme proposed by Dahlquist, Liniger and Nevanlinna has clear advantages in complex, stiff numerical simulations: unconditional $G$-stability for variable time-steps and second-order accuracy. Yet it has been underutilized due, partially, to its complexity of direct implementation. We prove herein that this method is equivalent to the backward Euler method with pre- and post arithmetic steps added. This refactorization eases implementation in complex, possibly legacy codes. The realization we develop reduces complexity, including cognitive complexity and increases accuracy over both first order methods and constant time steps second order methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
