Abstract
It is shown that semi-implicit time differencing on a nonstaggered grid using centered time and space derivatives leads to a decoupling into four separate solutions on different subgrids. This deficiency may be successfully overcome by combining weighted averages of Laplacian operators on the subgrids. However, a far more satisfactory approach is shown to be the use of a staggered grid which appears to be a natural choice for the semi-implicit scheme.