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This report considers linear multistep methods through time filtering. Theapproach has several advantages. It is modular and requires the addition ofonly one line of additional code. Error estimation and variable timesteps isstraightforward and the individual effect of each step\ is conceptually clear.We present its development for the backward Euler method and a curvaturereducing time filter leading to a 2-step, strongly A-stable, second orderlinear multistep method.

Analysis of the effect of Time Filters on the implicit method: increased accuracy and improved stability