This paper analyzes a $\theta$-method and 3-point time filter. This approach adds one additional line of code to the existing source code of $\theta$-method. We prove the method's $0$-stability, accuracy, and $A$-stability for both constant time step and variable time step. Some numerical tests are performed to validate the theoretical results.

翻译：本文分析了$\theta$方法与三点时间滤波器。该方法在现有$\theta$方法源代码基础上仅增加一行代码。我们证明了该方法在恒定时间步长和可变时间步长下的$0$-稳定性、精度和$A$-稳定性。通过数值实验验证了理论结果。