Analysis of the effect of Time Filters on the implicit method: increased accuracy and improved stability
For researchers using linear multistep methods, this provides a simple, modular way to achieve higher-order accuracy and stability without complex modifications.
The paper introduces a time filter that enhances the backward Euler method into a 2-step, strongly A-stable, second-order linear multistep method, improving accuracy and stability with minimal code addition.
This report considers linear multistep methods through time filtering. The approach has several advantages. It is modular and requires the addition of only one line of additional code. Error estimation and variable timesteps is straightforward and the individual effect of each step\ is conceptually clear. We present its development for the backward Euler method and a curvature reducing time filter leading to a 2-step, strongly A-stable, second order linear multistep method.