1549301742-The_Theory_of_Difference_Schemes__Samarskii

Economical factorized schernes 581

With this aim, the equation B1 B2 Ytt

that

Ay can be solved in such a way

In so doing three sequences of the values yj - l, yj and w( 2 ) are yet to be

saved in the storage in the process of calculations of yi +^1. One trick we have

encountered is connected with a prior reduction of the preceding scheme to

thereby increasing the total volume of computations, but saving only two

sequences of the values yj and w( 2 ).

The algorithm of solving equation ( 45) was demonstrated before and

so it remains only to construct economical factorized schemes associated

with problem ( 42) by means of the operator La acting in accordance with

the rule

and adopt as a primary one in that case

where

2

Ay = L (aaYx")xa'

0

Ry=-(} A y,

<>= l

The parameter (} is so chosen as to satisfy the stability condition

l+s

(Ry, y) >

4

( -Ay, y) ,

0 0
for any y E H = r2, where r2 is the set of all functions given on the grid
wh and vanishing on the boundary ih of the grid. True, it is to be shown
that the choice (} = (1 + s)c 2 /4 is sufficient for doing so.