(4.3)
() , () () :
. (4.4)
, (4.3) (4.4).
. :
(4.5)
h ( ). . R~(h2) . . h2.
(4.6)
(4.7)
. , . R ~ (h3). 34, h.
:
(4.8)
.
R~(h3) ,
.
(4.9)
, , R~(h3). - .
() h = const. R~(h5) . Yj(i+1) i+1 :
(4.10)
Yj; Fj (, Yj,). , j, .. .
.
(4.11)
R~(h5), :
(4.12)
h , ()= ' (0) =y0′.
, . ( ε = E = 10-3) , , () .
|
|
, yj ( i +1) h h/2. y*j ( i +1) yj ( i +1). | yj ( i +1) ̶ y*j ( i +1)|< , h, . , , , . R~(hs ) .
. 5. .
1. N, ε= . h = H =0, 1 (x0)=0, y2(0)=y2, , yN(x0)=yN
2. 5 j = 1, 2,...., N :
3. ( )
4.
, h 2 . 2, Yji. , xi+1=xi+h . , h . 2.
, Yj(i+1) .
, Rj(i+1) . E.
:
Yj(i+1) , : n = 4 () n+1. , Rj(i+1) Rj(i+1) > E, n , Rj(i+1) < E /20, . .
, , , , . ( ) .
. . . .
, , .
|
|
, ( ), .
.
. (4.2) () :
,
,
. 4.2.
. 4.2
(). Microsoft Excel VBA Microsoft Excel . u2(t). . .