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This paper analyzes a $\theta$-method and 3-point time filter. This approachadds 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. Somenumerical tests are performed to validate the theoretical results.

Stability and Accuracy analysis of the $\theta$ Method and 3-Point Time filter