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The authors show that the round-off error can break the consistency which isthe premise of using the difference equation to replace the originaldifferential equations. We therefore proposed a theoretical approach toinvestigate this effect, and found that the difference scheme can not guaranteethe convergence of the actual compute result to the analytical one. Aconservation scheme experiment is applied to solve a simple linear differentialequation satisfing the LAX equivalence theorem in a finite precision computer.The result of this experiment is not convergent when time step-size decreasestrend to zero, which proves that even the stable scheme can't guarantee thenumerical convergence in finite precision computer. Further the relativeconvergence concept is introduced.

The finite precision computation and the nonconvergence of difference scheme