  The authors show that the round-off error can break the consistency which is
the premise of using the difference equation to replace the original
differential equations. We therefore proposed a theoretical approach to
investigate this effect, and found that the difference scheme can not guarantee
the convergence of the actual compute result to the analytical one. A
conservation scheme experiment is applied to solve a simple linear differential
equation satisfing the LAX equivalence theorem in a finite precision computer.
The result of this experiment is not convergent when time step-size decreases
trend to zero, which proves that even the stable scheme can't guarantee the
numerical convergence in finite precision computer. Further the relative
convergence concept is introduced.
