1549301742-The_Theory_of_Difference_Schemes__Samarskii

688 Methods for Solving Grid Equations

Here the composition of the grid is

where /1i is its boundary. In that case

0

Ay=-Ay, yEH=Q,

and instead of (35) we obtain

(35') Ay=<p, y E fl,

where the right-hand side <p differs from the function f only at the near-

boundary nodes. Simple algebra gives

(36)

implying that

(37)

(

8 = 4 -1 ' srn^2 --7l" hl + -1. sin^2 --7l" h2 )

h I 2 2l I h 2 2 2! 2 ,

4 4

~ = h2 + h2.

1 2

Here we should take into account that

( a1 b (^1) + a2 b 2 )^2 < ( - a1^2 + a2 2) (b21 + b'22)
and