. , , . , , , .
, -, , . :
y= f (x,y) , ..
dx Yi Xi.
, .. (, ) .. h = xi+1 - xi .
, : x = x0, y(x0) = y0. , , .. x1 , y2 - 2 ..
() .
, , . , i f(xi, yi), h:
yi+1 = yi + ∆yi.
, f(xi, yi) ( , ).
, .
, ( ), .
,
-.
¢ = f(x,), , () (), 1- .
() (, b) = (), , ¢ (x) xÎ (,b). . (,y) = 0, , . (,y) =0 , .
¢ = f(x,) f(x,) D, (x,y), (x0,y0) Î D, 0 h £ £ 0 + h, () ,
|
|
() - .
.
, , .
= () [x0,X] :
yk+1 = yk + h×f(xk, yk), (1)
= (), +1 = xk + h, ( = ), k = 0,1,2,...n -1 h =
e h h2 < .
-
= () :
(2)
, , ,
h h3 < .
-
= () [x0, X] :
+] = yk + yk, k = 0, l, 2,...n l (3)
yk = (),
,
,
, , h =
h h4 < .
-
- , h 2h , - . , , :
(4)
k s = 2,3,4 , - , - . .
, 2h h (4). , (4) k.