1. This scheme would appear to have two virtues. The first is, linearl, the truncation error 0(h2), reduced hg a factor of 4 over either difference operator alone. The second is that the terms with one-quarter weights on either side of the firstorder upwind contributions (with weight one) are balanced. Since both sets of these terms with one-quarter weight are of themselves destabilizing, through the contribution of a wrong eigenvalue sign, balancing them with minimum weight for either can, on the a\rerage, be expected to minimize their adverse impact on robustness in the real case of variable coefficients. For this second-order scheme, the first-order upwind contributions to the diagonal are highly stabilizing in the sense of 'eonard.2s -4xisymmetric Flow Results
2. This work was partially supported by NASA Ames Research Center under Contract NAS2-11920, by AFOSR under Contract F4962G83-C-0084 and by ARO under Contract D-L4G29-84C-0002.