Abstract: By the so-called "first-forward-then-centered difference analogue" for the equation of the form ∂ζ/∂t+u∂ζ/∂x=0 in conventional operation,in meteorology,is meant an analogue,in which the space derivatives are replaced by centered differences,but the time derivative is replaced by a forward difference at the first time step and then by a centered difference.For the sake of investigating the computational stability and convergence of this analogue under two arbitrary initial conditions an analogue with centered differences in both space and time is discussed.The results show that the analogue is stable when and only when the conditions:λ(=uΔt/Δs)1-λ2 being fiaite,are exactly satisfied,where u the velocity of the basic current;Δt andΔs are time step and grid length respectively.However even in a stable case,the difference solution so obtained can not converge to the corresponding exact solution,unless the value of vorticity at the end of the first time step,i.e.ζ(1),is convergent.For the convenience of comparison,three difference analogues used to compute ζ(1) are investigated.It is found that the conventional analogue is the worst one of them and when λ→1-0.it is computationally unstable.If any one of the other two up-wind analogues is used in this case it is computationally stable.