, (6). , , ( ) ( ).
, .. .
. : I ; II ; III , . , , .
.
u = u (x, t) (t = 0):
u (x,0) = (10)
I III.
1. ( )
(t) (11)
- , T , . , .. .
2. ( ) . , x = 0
(12)
. t) , .. , x = 0 . (0; Δx) t, (4)
Δt Δx 0,
, (12),
x = 1 ,
, , , . , , (t) = 0 (t) = 0, ,
= 0
3. ( ) . , x = l
(13)
(13) , .. . ; . , , , :
q =α(u θ),
α - ( ).
|
|
, c .
q(t),
x = l,
q =α(u(l, t) θ(t)).
, .
,
, .
, , u (x t), . , . , u (x, t), , .
(11), (12), (13) , , . (10).
, u = u (x, t)
0<x< l, 0<t T
u(x,0) = 0<x< l,
u(0, t) = , 0<t T
x = 0 x = l.