, ν. , t
(t) = 1 -
g(t) = :
- .
- k , .
- .
.
Δt . . :
- t . Δt .
(t) (1)
- t . Δt , .
(t) (1 - ) (2)
(t) , .
,
(t+ Δt) = (t) + (t) (1 - ) (3)
(t+ Δt) - , (t + Δt)
;
(t) - ;
- Δt
;
(1 - ) - , Δt
.
≈ 1 - λ Δt + ,
1 - ≈ νΔt + ,
Δt. (3) , ,
′ (t+ Δt) = (t) (1 - λ Δt) + (t) νΔt (1 - λ Δt). (4)
(4) Δt
(t+ Δt) - (t) = - (t) λ Δt + (t) νΔt - (t)∙νΔt∙ λΔt). (5)
(t)∙νΔt∙ λΔt Δt∙Δt = Δt , , Δt ≈0, (t)∙νΔt∙ λΔt ≈ 0.
(t+ Δt) - (t) = - (t) λ Δt + (t) νΔt. (6)
(6) Δt
= - (t) λ + (t) ν.
, Δt → 0,
() = (t) = - (t) λ + (t) ν. (7)
. :
|
|
- t k . Δt .
(t) (1 - λ Δt)(1 kνΔt); (8)
- t . Δt , .
(t) λ Δt (1 kνΔt); (9)
- t . Δt .
(t) (1 - λ Δt)(1 + k) νΔt. (10)
(t+Δt)= (t)(1-λΔt)(1kνΔt)+ (t)(1 kνΔt)λ Δt+ (t)(1-λΔt)(1+k)νΔt. (11)
(t) = - (λ+kν) (t) + λ (t)+ (t) (k+1)ν. (12)
0≤ k≤ n.
.
- t . Δt .
(t) (1 nνΔt); (13)
Δt → 0,
(t) = - nν (t) + λ (t). (14)
, , n .
(t) = - (t) λ + (t) ν.
.
(t) = - (λ+kν) (t) + λ (t)+ (t) (k+1)ν. (15)
(t) = - nν (t) + λ (t).
.