**Numerical Solutions Applied To Heat Transfer And Fluid
Mechanics Problems**

Allen's method does not generate an error estimate like DEM. Taylor series expansions must be substituted into the final difference equation. This produces the terms from the original PDE evaluated at the expansion point, and error terms. I have provided some Mathematica input files that perform such substitutions for some specific difference equations associated with transient fluid flow (math.in, math1.in and math2.in)

Obtaining the finite different approximation and error terms with DEM involves
more algebra than you want to do by hand. I've provided two sample
MathCad files (DEM1.mcd and DEM2.mcd) that generate difference equations
and error terms. If you don't have MathCad on your computer, you can view
what I've done in DEM1.pdf and DEM2.pdf.