1549301742-The_Theory_of_Difference_Schemes__Samarskii

288 Difference Schemes for Elliptic Equations

for v = k 12 u,, 2 yields

Likewise,

from which estimates (33) follow in1mecliately.

When CY = {3 = 1 and CY = /3 = 2 we n1ight have

where

From the preceding relations it seen1s clear that Acx" 11. - Laa ·u = O(h~),
CY = 1, 2. Thus, the differential operator (30) is approximated to second
order by the difference operator

2

A y = L Acx(3 y ,

cx,(3=1

meanmg

Au - Lu= 0(1h1^2 ).

In addition to operator (32), we take into consideration one more operator

with the values

2

Ay = L Acx(3 y,

cx,(3=1

providing an approximation of 0(1h1^2 ).