, , . , . . , , .
, , , , . , , , .
, . :
(1)
, b f () x .
, , . (1), , . [1].
. I , f (), = = b. I, b , , , .
.
1. ; . , , , , , . ().
2. ; , . .
. , , . .
(1), . 1. n , h-(b-a)/n. , . 2,
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. 1. .
. 2. , . 1.
.
. , = f () xi xi+1,
h , ABCD. yt = f (xt), ABED yth, ,
. (2)
(3)
0 = n = b. , (2) (3),
(4)
; , (1) . . , , , , - . , , ( , ). , , = f () ; , .
(4) , = f () , i yi+1 (BC . 2). , = f (x) xi , xi+1. , , (4).
= f (x) x = xt. , f() , .
(5)
, xi+1,
(6)
, (5) (6) , , . :
ydx xt xi+1,
(7)
. , . , (7) , h .
(8)
h , , . , , ' - df/dx xt h2,
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, y''h3, (8). .
,
(9)
. , , K; , " xt xi+1.
K. , (7) . , . .
= , , = ; , . = 2.
(10)
(7) (8) yi+1 = (xi + h)2
(11)
(10) (11) , ' = 2, (9)
K
(12)
(13)
b df/dx = b ' df/dx x = .
= 3 , . , K , h3, (9) , " .
.
,
(14)
, ,
, (13) , .