1549301742-The_Theory_of_Difference_Schemes__Samarskii

Two-layer iteration schemes^675

Table 5

k 1 4 5 6 8 9

t:,. k 39.6 4.7 7.4 3.2 1.1 6.7

k 10 16 17 18 24 25

t:,. k 3.2 0.2 3.1 1.5 0. 1 0.8

k 26 32 33 34 48 49

t:,.k 0. 1 0.04 0.3 0.14 1.5' 10-^3 1.3' 10-^2

k 50 56 57 58 59 60

t:,. k 6.7' 10-^3 2.2. 10-^4 1.5' 10-^3 7.2' 10-^4 6.5' 10-^4 2.1' 10-^4

k 61 62

t:,.k 1.1' 10-^4 8.7. 10-^5

In that case we are looking for a solution to the system of equations

X; = ih, i = 1, 2, ... , N - 1,

h = 1/ N, v(O)=l, v(l)=O,

under the following conditions: N - 1 = 19, c = 10-^4 , n = 64 = 26. The

chain in question

is constituted in agreement with formula ( 44) and it reveals a nonmonotone
character of convergence of the iterations. True, it is to be shown that
during the transition from the kth iteration ( k = 4j) to the ( k + 1 )th
iteration (k + 1 = 4j + 1) the error of approximation t:,.k = llY1.: - Yk-illc
is being increased and, after this, is held clown in passing to k = 4j + 2,
4j + 3, 4j + 4.