Abstract
The-ε-stability of a scheme implies the stable calculation of all computable Fourier components corresponding to the wave lengths shorter than the threshold wave length datermined by positive small number ε. The considered schemes employ the equi-distant five points difference formula for the space discretization, and the forward difference formula for the time discretization. The results of our numerical experiments are shown, which were set especially to see the effectiveness of the third order upwinding difference formula of kawamura type in comparison with that of standard type in the view point of ε-stability. A result is added concerning the maximization of the stability limit with respect to time mesh through the control of the coefficient of the fourth order artificial diffusion term for each fixed ε∈(0, 1].
