2) 1, 2 .. S (z) (4.33) S ().
, , . .
(4.32).
() .
1. (4.32), z :
2.
3. u (z) ε (z)
, .
4. ()
(4.35)
(4.35) , () (-1) ε (-1) , 2 (-2) ε (-2) 3 (-3) ε (-3) . .
5. () (4.35) , .4.26.
1. .
2. - .
3. " " ?
4. .
4.10.
,
, , , , . , 4.4, , 4.9. , .
, . , . , z- , , . . . .
|
|
1. -
W (p) -, u (t):
(4.36)
(4.37)
t, Δt . .
, (4.38)
-1 .
(4.38) (4.36)
, (4.39)
-
(4.40)
(4.40) , , , -. , , z -. (4.38) . , , (4.40) .
- (4.38), - (4.37). (4.40) , , ε. -. , .
, - t=0
t=0, , , .
- =0, 1, 2, (4.40):
0 | u0 = 0 + bT +a (1-0) =a+bT | |
1 | u1 = u0 + bT +a (1-1) =a+bT+bT | |
2 | u2 = u1 + bT +a (1-1) =a+bT+2bT | (4.41) |
: | : | |
-1 | un-1 = un-2 + bT +a (1-1) =a+bT+ (n-1) bT | |
un = un-1 + bT +a (1-1) =a+bT+nbT |
(4.41) .
(4.37) -. (4.37) t :
u (t) un - .4.27. - (t)= a+bT+nbT- a+bnT=bT. -.
b, . b -. un (t) un .
|
|
, bT - . , , . -. z -, .
2. ()
. 2- .4.28.
(4.42)
(4.43)
(4.42) (4.38) (4.43).
.
, , , , , , , .
1. , . .
2. 1- , ? - ?
3. ? ?
4. ?
5. 2- , ? - ?
5.
5.1. .
, , , , , , ... .. .
1. (min L) (.5.1).
(), L . (.5.1) : 1, 2 3 2. , , (.5.1), , , , , , .
2. , .. , , .. , W (min W), .. , .
3. ... , . ...
|
|
, , . , . , : y=f (x). , () ( 1), ( 2), ( 3) .. ( ), : 1, 2, 3 ..
, .
(5.1)
F , , . J , .
y=f (t), J . . , 1 , , 2 , , 3 , ..
. : .
,
: = (t) J, ( ):
(5.2)
.
(.5.1), .
.5.1
.
F
(5.3)
(5.3) (5.2)
,
, . .
, . . , (t) : .
1- , , . .
|
|
, , .. , (5.2), . (5.1), , ( ) ():
- - (5.1).
(5.1) . () , .
, 1, 2, ( ), F ( F )
(5.4)
t, .. 1, 2n, (5.4) J. :
( ) , yi (t), (5.4), . , n 1, 2,, n, (5.4), , k , m l :
(5.5)
m L, :
(5.6)
λ1, λ2,,λk , λk+1 (t),, λk+m+l (t) - t. n k+m+l λ (t) n+m+k+l : n k+m+l (5.6).
, , :
:
,
2n. (t) 2n , , , (t) (-1) t1 t2.
, (t) .
, (t), , .
( ) :
1. . , .
2. . (5.1) , (t), (5.1), . .
3. . , "" .
. , "". : "" .
, , " ", . ti -:
ti-0 , t, ti , ti+0 , t ti . - , (t) .
|
|
,
(5.7)
. (. 5.8).
1. .
2. ?
3. ?
4. , .
5. , .
6. , .
7. , .
8. , .
5.2.
α
(5.8)
, ,
(5.9)
, ,
(5.10)
(5.11)
( ω)
(5.12)
(5.12)
(5.13)
(5.13) (5.9)
(5.14)
, (5.13), (5.14).
1, 2 λ 0 ω 0 ω Q.
, : ω 0= ω =0. (5.13) :
(5.15)
(5.15) (5.13) (5.14)
(5.16)
i ( t=0) . (5.16) : λ0<0.
λ 0 =0 (5.10):