1549301742-The_Theory_of_Difference_Schemes__Samarskii

Other problems^193

Substitution of wj+i = b;+i (v;+i - vj)/h into (47) leads to the relation

(48)

Recalling that vN = 0 and summing equalities ( 48) over j = i, i+ 1, ... , N -

1, we obtain

(49)

Substituting 1/;k = ~ 1Jr k + ij;k* into ( 49) yields

7' k '

in light of the relations

0

77;+1 = r;+1/2 111+1/2'

Furthermore, we might have

h^2 v

8 rj+1/2 aj+1

As a final result we get the inequality

j

I: h = T'j < 7'j+1/2.

k=l

h

=-lvl. 4 c

1

(50) I I

Rh v 1 N-1 o o R

llvllc < 4 c

1

• ~ t-; h(l 771+1 I+ I hi I)+ ~llr1/J* lie·