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: . : 04.06.2012. : 2010. : 16. antiplagiat.ru: < 30%

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2

1.




:
x5m+10 = x5m0 + h4m0*F(x5m0, t4m0)4,0 (1)
-
x'(t4m0),.. 1 (s=1).
-
Ӡ x' = F(x, t) (x5m0,t4m0):
x' = A*x, (2)
(x5m0,t4m0).

t4m0 h4m0 -
. , -
, (2) . -
,.. -
m.

:
1. _ ..
: = *7l0*Р5-10
젠 y = P5-10*x , (2) :
y' = 7l0*y (3)
(3) :
y5m+10 = y5m0 + h*7l0 * y5m0, (4)
h*7l0 .
-
(4) :
1 + h*7l0 - r = 0.
:
r = 1+ h*7l0,
7l0 =7 a0 _+.7 b0 .
_ 1.. (3) -
, .. -
7 a0 < 0.

(4) , 1 , (0, -1).
, h -
, .
:
h < 2*7t0, (5)
7t0=1/72a20 - (3) . -
. -
T40 = 3*7t0 , 7t0 = 72a25-10.
, (3) n- ,
T40 > 3*7t4max0,
7t4max0 = 72a4min725-17 0; 7a4min 0= min 7a4i0 . 7a4i0 (i=[1;n]) -
: max72a4i720=7a4max0 :
7t4min 0= 1/7a4max0,
:
h < 2/7a4max0 蠠 h < 2*7t4min0.
_ 2.. (2) -
, .. 7a0 > 0 . .. , .. 720r720>1.

. :
720 1+h*7l0 72 0<7 2 0e5hl7 20 (6)

2. _ ..
(1)
x(t4m0+1) h .
t [t4m0 , t4m+10],
Š4i5am0 =1/2! * h4m520*x4i0''(t),
i=[1;n].

3. _ ..
(5)
(6) .
:
h < 2*7t0 .
n- :
h4i0 <= 2*7t4i 0.
:
h < 2*7t4min0 , 7t4min0 = min 7t4i
, -
:
1) (1) x5m+10;
2) dx4i5m0 = x4i5m+10 - x4i5m0 ;
3) :
h4i5m0 <= E4i5a7/0[720f4i0(x5m0,t4m0)720 + E4i5a7/0h4max0] (7)
4) m- :
h4m0 = min h4i5m0.


-

- 1- .
- 2- 4- ,
s ,
.
, h4m0.
- 2- :
x5m+10 = x5m0 + h4m0/2 (k410+k420),
k410=f(x5m0,t4m0) ; k420=f(x5m0+h4m0*k410,t4m0+h4m0).
Š5a0 = k*h4m530 .
- 4-
x5m+10=x5m0+h4m0/6(k410+2k420+2k430+k440),
k410=f(x5m0,t4m0); k420=f(x5m0+h4m0/2*k410,t4m0+h4m0/2); k430=f(x5m0+h4m0/2*k420,t4m0+h4m0/2);
k440=f(x5m0+h4m0*k430,t4m0+h4m0).
Š5a0 = k*h4m550.



" -
" . "" , 7 0 (7l4max0)
(7l4min0) ,
x' = A*x (1)
,
. -

h <= 2*7t4min ,0 (2)
7t0=1/72a20 - y' = 7l0*y .
. (2)
, -
.
:
x5m+10 = x5m0 + h4m0*F(x5m+10, t4m+10) 4 0(3)
h4m0 , x5m0 5m+10 . -
x5m0 , , x5m0
x5m+10 .

-
Ӡ x' = F(x, t) (x5m0,t4m0):
x' = A*x,
(x5m0,t4m0).

t4m0 h4m0 -
. , -
, (1) . -
,.. -
m.

:
1. _ ..
: = *7l0*Р5-10
젠 y = P5-10*x , (3) :
y' = 7l0*y (4)
(4) :
y5m+10 = y5m0 + h*7l0 * y5m+10, (5)
h*7l0 .
-
(5) :
1 - h*7l0*r - 1 = 0.
:
r = 1/(1-h*7l0) ,
7l0 =7 a0 _+.7 b0 .
_ 1.. (4) -
, .. -
7 a0 < 0.

(5) . , h
,
.
:
h < 2*7t0, (6)
7t0=1/72a20 - (4) . -
. -
T40 = 3*7t0 , 7t0 = 72a25-10.
, (4) n- ,
T40 > 3*7t4max0,
7t4max0 = 72a4min725-17 0; 7a4min 0= min 7a4i0 . 7a4i0 (i=[1;n]) -
: max72a4i720=7a4max0 :
7t4min 0= 1/7a4max0,
:
h < 2/7a4max0 蠠 h < 2*7t4min0.
_ 2.. (4) -
, .. 7a0 > 0 . .. , .. 720r720>1,
:
720 1/(1-h*7l0) 720 > 1.
-
:
720 1/(1-h*7l0) 720 >7 2 0e5hl7 20. (7)
, 720h*7l20 -> 1
. , -
, 1 ,
(0, 1), (7) .

2. _ ..

, :
Š4i5am0 =-1/2! * h4m520*x4i0''(t),
t4m0 <= t <= t4m+10,
i=[1;n].

3. _ ..
(6)
(7) .
:
h < 2*7t0 .
n- :
h4i0 <= 2*7t4i 0.
- -
. .
, -
, . ,
,
. ,
, -
. :
E4i5a0 <= 0,001 720x4i724max0,
i=[1;n].

:
1. (3) x5m+10 h4m0,
x = F(x,t) ;
2. :
Š4i5am0 = 720h4m7/0(h4m0+h4m-10)*[(x4i5m+10 - x4i5m0) - h4m7/0h4m-10*(x4i5m0 -x4i5m-10)]72
3. -
. Š4i5am0 < E4i5a0, , -
,
.1.
4. :
h4i5m+10 = SQR(E4i5a7/20Š4i5am720) * h4m0.
5. X :
h4m+10 = min h4i5m+10.
6. .



-

- 1- .
- 2- 4- ,
s ,
.
, h4m0.
- 2- :

x5m+10 = x5m0 + h4m0/2 (k415m+10+k425m+10),
堠 k415m+10=f(x5m+10,t4m+10); k425m+10=f(x5m+10-h4m0*k415m+10,t4m+10).
Š4m5a0 = k*h4m530 .
- 4-

x5m+10 = x5m0 + h4m0/6 (k415m+10+2k425m+10+2k435m+10+k445m+10),
堠 k410=f(x5m+10,t4m+10); k420=f(x5m+10-h4m0/2*k415m+10,t4m+10-h4m0/2);
k430=f(x5m+10-h4m0/2*k425m+10,t4m+10-h4m0/2); k440=f(x5m+10-h4m0*k435m+10,t4m0).
Š5a0 = k*h4m550.


2.




X5m+10=X5m 0-5 0J5-1 0*5 0(X5m0)5 0*5 0F(X5m0),
J(X)=F4x5|0/4x=xm
:
1. . , P(G4x5|0(X5*0))=0
G(x)=X - J5-10(x) * F(x) - -
. : P(G4x5|0(X)) < 1
X5m0.
F(x):
X, X5*0.
. ,
X5*0, .
2. X500 -
. -
F(x) X5*0: , ,
-
X500 X5*0.
3.
E5m+10 = C4m0 * E5m051+p0, 0 < P < 1.
X -> X5*0 P -> 1. , -
. ,
6-7 .
4. - -
, X F(x).




1. J=F4x5|0.
:
- . , -
, -
.
- - :

dF4i0 F4i0(x410,...,x4j0+dx4j0,...,x4n0) - F4i0(x410,...,x4j0-dx4j0,...x4n0)
--- = --------------------------------------------------
dX4j0 2*dX4j

,
. -
, dX4j0 X5*0.
2. J5-10 -
, :
dX5 0=5 0J5-10(X5m0)5 0*5 0F(X5m0)
J, :
J(X5m0)5 0*5 0dX5m 0=5 0F(X5m0)
M- J F . dX5m0,
,
X5m+10=X5m0+dX5m
- ,
.



t - , 0 1.

H(X,t)=0,
, :
1. t=0 X50
2. t=1 X5*
3. - H(X,t) t.
,
H(X,t) = F(X) + (t-1)

H(X,t) = t * F(X)
, - -
1-3.
:
t410=7D0t H(X,t410)=0 X500. -
X5t10.
t420=t410+7D0t H(X,t420)=0, X5t20
, .
..................



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