[0, X] - . 0 < 1 <... < xn = - .
xi .
:
, [0, X], - , y1, y2,,yn - .
, . .
,
= f(x) .
- .
(), = f(x) . , . , - .
, yn+1.
, yn+1.
.
- .
. . .
:
Y = f(x, y)
y(x0) = y0
h :
xi = 0 + ih yi = y(xi), i = 0, 1, 2,...,
xi - ,
yi - .
2.
(xi, yi) α. tg α = f(xi, yi)
, . , .
yi+1 = yi + Δy
ABC
tg α = f(xi, yi) .
Δ = h ∙ f(xi, yi).
yi+1 = yi + Δy, . :
.
2. .
, . , , .
- 3.
|
|
F(x, ) -
|
:
|
;
|
y(x0) = y0;
|
:
-
|
3. - .
- . . 2 i-o ε. .