Abstract:
The Halfway Way
Catalin Trenche and John Burkardt

An alternative formulation of the midpoint method is employed to analyze its
advantages as an implicit second-order absolutely stable timestepping method. 

Legacy codes based on the backward Euler method can be upgraded by inserting 
a single line of new code. 

Local truncation error can be well estimated, allowing for adaptive timesteps.

We present some specifics of implementation, conservation, error estimation,
adaptivity, stability, and performance on several test problems.