Analysis of Forward Euler Method with Time Filter

This papers examines the impact of augmenting the new explicit Euler method with a simple time filter. The modification is fully modular, requiring only a single additional line of code, and can therefore be incorporated easily into existing computational frameworks. The resulting scheme admits straightforward stability analysis and provides an immediate estimation for error, while the role of each stage in the algorithm remains conceptually transparent. Applying the time filter to the forward Euler update yields a method that is algebraically equivalent to a two-step, second-order linear multistep scheme of leap-frog type