1549301742-The_Theory_of_Difference_Schemes__Samarskii

Some properties of difference elliptic operators 287

In this line, the operator Laf3 u is approximated by the difference op-

erator

(32)

which is defined for CY -::/- f3 on the 7-point pattern (see Fig. 15) consisting

of the nodes

Figure 15.

The operator Aaf3 arranges itself as a sum

We are going to show that A~ 2 and A 12 have the first and second order of
approximation, respectively:

(33)

Indeed, we refer to the operator A~ 2 u = (k 12 u;;Jx 1 • Substituting here the
expressions

OU h2

u. = --- -

X^2 OX 2 2