.
()
. , (..) 1.2, 1.1. [0;T] , 1.6.1,
(1.6.2)
t [0;T]
1.1 f(u,t) t u t [0,T](.. u). u(t), .. 1.2.
1.6.1. .
n, s <=n<=s-1
1.2 f, T>0, , u(t) t [0,T]
a) u(0)=u0
b) ut(t)=f(u(t),t) t [0,T]
u k->0, t [0,T]
1) 1.6.2 k->0 t... v(t) , k t/n. ,
2) ..
, ,
3) ; . , ,.. , 1.6.1, .
4), 1.6.1 , o(1) O(k). O(k^2) . : s , θ(k^-1) . 1
. ó
, . p 1.6.1
(1.6.4)
, (smooth) 1.2, ,
. .. 1.2, 1.1. [0,T], , f(u,t) p u t. >=p c 1.6.4..
(1.6.5)
t [0,T]