10. 1
, .
.
10.2
10.1
a | b | Δdop | |||
0.2 | 1.6 | 0.05 | |||
0.2 | 0.5 | ||||
0.5 | 0.9 | ||||
0.01 | |||||
0.02 | |||||
0.02 | |||||
0.015 | |||||
0.5 | 0.003 | ||||
0.5 | 0.07 |
10.3
- , (. . ), . .
: , ( ).
1 , ,
(1)
( ) - .
( ) (1) y = j(x), , .. , (1) . .
y = j(x)+const, (2)
, , . . .
' (x)=f (y(x),x) (4)
x=x0 y(x0)=y0 (5)
y(x) x0 b.
:
- , ;
- , .
.
.
.
[a, b].
( ) . |
[a,b] n , x0, x1,..., xn, xi = x0 +i×h (i=0,1,,n), - . ( ) 0 (x0,y0). y =j(x) 0 x=x0 (.10.1)
|
|
x=x1 1 y1=y0+h×tga0. tga0=y(x0) , (4), y1=y0+h×f(x0,y0), f(x0, y0) - , 0. 1, 2:
y2=y1+h×f(x1, y1).
i- yi+1=yi+h× f(xi,yi). () [a, b] ( h ),
.
i - , , Ai (=xi), yi+1/2, h, Ac (=xi+1/2) [ xi, xi+1 ] (.10.2.):
fi+1/2 Ac (=xi+1/2=xi+h/2): |
Ai+1 h Ai:
, Ai+1:
.10.2 E = xi+1 , Ai+1.
.
yE E (.10.3.): yE=yi+h×f(xi, yi).
E fE=f(xi+1,yE).
h f(xi, yi) fE, .. Ai+1,
.
, Ai+1: |
.
(h3), - (h2).
10.4
1- [0,4], Δdop=0.04.
y(x)=exp(x2∕4)
1.
( ) x [a,b] |
% |
3. 1-
% |
4. |
|
|
% |
.
h. n=2n d . , 256 ,
5.
(.10.4) (.10.5)
.10.4 .10.5
, .
:
[a,b] , . .
10.5
1. .
2. .
3. .
4. n, (dM1)<Δdop
5. .
6. .
7. .
10.6
1. .
2. .
3. . .
4. .
5. .
10.7
1. .., .., .- , ,1970 .-664 .
2. .., .., .-.,,1972 .-368 .
3. .., -, ,2003 .,-232.
4. .., Mathcad 11.-, ,2003 .-560 .