1549301742-The_Theory_of_Difference_Schemes__Samarskii

646 Methods for Solving Grid Equations

Also, it will be sensible to deal with the newly formed vectors

j=l,2, ... ,N2-l,

Fj = (P1j, {t2j> ... , μN1-1,j), j = 0, Nz,

and a difference operator C acting in accordance with the rule

(CY1) z = (2y-h;Yx- 1 xJ 2 1 , 0 < i < N1, Yo 1 · = YN 11 · = 0.

Fro1n such reasoning it seems clear that problem (2) in view is tantan1otmt

to the systen1 of vector equations (.3).

Let N2 = 2" for the clarity only. The inain idea behind the cleco111-

position method is the further successive elin1ination from the governing

equations of the vectors Yj with odd numbers and, after this, with even

numbers divisible 2, 4, 8 etc. Other ideas are connected with setting the

following equations for j = 2, 4, 6, ... , N 2 - 2, where N 2 = 2":

Applying the operator C to the second equation and summmg up three

resultant equations yield a revised "short" system

Yo=Fo,

containing only the unknowns with even numbers and involving the mem-
bers

yCJ) = y(O) + C(OJy(O) + y(O)

1 1-1 1 1+1'

C(O) = C,