1549301742-The_Theory_of_Difference_Schemes__Samarskii

710 Methods for Solving Grid Equations

Adopting those ideas, the frainework of ATM (see Section 7) involves the

operator B = (E +w Ri) (E +w R2). By going through the matter chrono-

logically we rely on A = Ai + A2 with the members

A2 Y = - ::~ ( (~~ Ycca + 2 ~2 (a~ -Cla))

The operator D arose in Section 8, by means of which it is plain to fol'm

B = (D + w Ai) D-i(D + w A 2 ).

No wishing to covel' the computational procedures of MATM once

again, we fill in the table on the basis of numerical experiinents for c = 10-^4.

Table 6

c2/ Cl h=l/32 h=l/64 h=l/128

MATM ATM MATM ATM MATM ATM

2 20 23 28 32 39 45

8 23 46 33 64 47 90

32 25 92 37 128 53 180

(^128 26 184 39 256 57 360)
(^512 26 367 39 512 59 720)
Fron1 here it is easily seen that MATM offers more advantages not only in
an arbitrary domain, but also in the case of variable coefficients.
10.4 ITERATIVE ALTERNATING DIRECTION METHODS

1. The alternating direction n1ethod for solving the difference Dirichlet
   problem in a rectangle. So far we have considered the Dirichlet problem
   for Poisson's equation in a rectangle G = (0 < J,'a <la, C\' = 1, 2):

C\'=l,2,