The Dirichlet difference problem for Poisson's equation 249intersection of the straight lines x~") = iexhex, CY= 1, 2 with the boundary
r of the domain Gare called boundary nodes along the direction Xex·
We denote by lh ex the set of all boundary nodes along the direction xex.
Let /h = /h '
'^1 + ih '^2 be the set of all boundary nodes. It represents such
nodes that are boundary at least with respect to one direction xex. The set
of all inner and boundary nodes is known as a grid wh = wh + ih in the
domain G (see Fig. 11).2 21Figure 11.
We offer below more a detailed classification of inner nodes. With this
aim, let us draw up a straight line parallel to the axis Ox ex through an inner
node x E w h. Its intersection with the domain G is an interval (or several
intervals), whose ends are boundary nodes along the direction Oxex. The
nodes from this interval can be distinguished by the approved rules. We call
the nearest to the end of the interval node a near-boundary node along
the direction Ox ex (with respect to x ex). If the distance to the boundary /h
is h~ f hex, any such node is said to be irregular with respect to xex. Let