Time filters increase accuracy of the fully implicit method (Q1647656)

The authors study the effect of adding a simple time filter to the fully implicit (or backward) Euler method. The approach requires the inclusion of only one line of additional code, where a straight forward error estimation is applicable and is adaptable to a variable time step. It is shown that the backward Euler method with a curvature reducing time filter induces an equivalent \(2\)-step second-order \(A\)-stable linear multistep method. Numerical experiments using benchmark problems show good accordance with the proposed method.