The summarized approxiination method 637reduces to successive solution of the syste1n of 2p equations(85 ) l 2p av 8t = L-er v + r-CY ' ij+(n-l)/(2p) < t < ij+o/(2p)'
l 2 P 8v ot = L o: + v + f+ " ' t j + l -o: I ( '2p) < t < t j + 1-lo-i l I ( 2p l ,
CY=l,2, ... ,p.
The usual starting procedure is connected with approximating the operators
L; by the difference operators A; acting in accordance with the rules0: p
A-;, = L A:(3 , At= L At(3,
(3:= 1 (3 :=o:In this regard, it seems clear that the operator L"'t; is approximated to
second order by the difference operator A;, the structure of which involves
the coefficients k!f3 taken for all c~ and f3 either at one and the sa1ne 1noment
t = tj+l/ 2 or at any another moment t* E [tj, tj+il· With these 1nembers,
the additive scheme in question acquires the forn1
a
(86) = L A:(3y)+f3/(2p)+(1.p:y+a/(2p) 1
T (3:=1pTL At(3 yj+f3i/(2p) + (1.pt)j+o:i/(2p),
f3=aCY= 1,2, ... ,p,
where CY 1 = 2p + 1 - CY and {3 1 = 2p + 1 - {3. Also, we should indicate the
direction of index account: CY 1 is being increased fro1n p + 1 to 2p along
with decreasing CY in reverse order fro1n p to 1.
The usual boundary conditions are imposed on the boundary x E if:
yj+o:/(2p) = μj+o:/(2p) for x E /1i, a CY= 1,2,.,, ,p,
(87)
yj+ai/(2p) = 11 j+aif(2p) for ;r E /~^1 , Cr 1 =p+l, ... ,2p.