The effect of round-off errors on the numerical solution of the heat
equation by finite differences can be theoretically determined
by computing the mean error at each time step.
The floating point error propagation is then theoretically time linear.
The experimental simulations agree with this result for the towards
zero rounding arithmetic.
However the results are not so good for the rounding to
the nearest artihmetic. The theoretical formulas provide an approximation
of the experimental round-off errors. In these formulas the mean value
of the assignment operator is used, and consequently,
their reliability depends on the arithmetic used.

Keywords:
Floating point arithmetic, numerical error propagation,
partial differential equations, finite difference methods