, - , . , , .
:
y¢ = f(x,y). (65)
y= y(x), . (65) , .. yi xi.
, :
y¢ = f (x,y), (66)
x=x0
y(x0) = y0. (67)
(66) x x+h ( h ), :
. (68)
, (; , ; ..) .
, .. (x, y) , .. x : h = xi+1 - xi.
: . y= y(x) , . , .
. y yi f(xi , yi), y() h:
yi+1 = yi + Dyi. (69)
- [6, 7]. .
h :
, (70)
x ;
n - .
y=y(x) x0+h. , y(x0+2h). y(x) . y(x0+ih), y=y(x).
(66) .
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y=y(x) :
yi+1 = yi + h f(xi, yi), i = 0, 1,..... (71)
(67).
35 . (xi , yi) y=y(x) , ai. ai (xi , yi), .. tg ai = f(xi , yi).
35
- 36.
36 -
(. 35). h2.
. :
yi+1 = yi + h f(xi + 0.5h, yi + 0.5h f(xi, yi)), i = 0, 1,..... (72)
37 (72). (xi , yi) L1 ai (tg ai = f(xi , yi)) (xi+0.5h, yi+0.5h f(xi, yi)). , L2 , .. tg bi = f(xi+0.5h, yi + 0.5h f(xi, yi)). (xi , yi) L2 L , xi+1. y=y(x) yi+1 x=xi+1, (72).
37
- 38. h3.
(66)-(67) - . . (66), , .
38 -
:
,
k1 =h f(xi , yi), k2 =h f(xi+0.5h, yi+0.5k1), (73)
k3 =h f(xi+0.5h, yi+0.5k2), k4 =h f(xi+h, yi+ k3), i = 0, 1,.....
- - 39.
- h5.
39 - -
1. .., .. . .: , 1991. 124 .
2. .. . .: . ., 1990. 544 .
3. .. . .: , 1987. 240 .
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4. .. , . : , 1991. 272 .
5. TURBO PASCAL: : . .: ., 1992. 247 .
6. .., .. . .: , 1999. 256 .
7. .. . .: , 1999. 408 .
8. .. . : : . 1999. 84 .
9. .., .. . -: , 1978. 1978. 176 .
10. / .., .., .. . -: , 1985. 165 .