, (6)
y(t), K(t,s) , x(t) , λ .
(6)
, (7)
, X . , λ, K(t,s) , F λ. (6) , :
(8)
(8) (6) , n -
, (9)
- , .
1
: , 2- C[0, 1], [0, 1] . , : +
:
C[0, 1]. , .
F(x) = + ;
= = ≤ = .
≤ 1 => ≤ .
.. ≤ .
, . ( = 0, = , = 1):
≤ 0,001 => ≤ .
, .
(t) = 0.214239 t1/3+t2
1: x(t) (Wolfram Mathematica 7.0):
Clear[x,t];
x[t_]=0;
For[i=1,i<=8,i++,
x[t_] = 0.5*Integrate[(t*s)^(1/3)*x[s], {s, 0, 1}]+t^2;
];
Print[x[t]];
. C = , .
, :
(1.1)
= 4.6E-5 ≤ 0,001.
[0, 1]. :
= = ≤ 1.
.. F(x) [0, 1] ≤ . . , :
< 0,001 (1.2)
: = < 0,001.
.. n = 6 .
2
: 0,01:
. (2.1)
. , :
(2.2)
, B[ , ] F F . .. F , .
= - . = -1, :
(2.3)
= , . :
(2.4)
, , r = 1. [-2, 0] F, F , = . :
|
|
(2.5)
n = 6 .
:
2: (Wolfram Mathematica 7.0):
Clear [F, x];
F[x_]=(1./8)*(-2*x^2-5);
x = -1;
For [i=1, i£6, i++,
x = F[x];
];
Print [x];
, . .
: , .
3
: , f . , = , = 0, .
= [-1, 1], .
: , f .
= ≤ .
f .
:
= 0,
= ,
= ,
= .
:
= = 0.3363.
4
: , F: X -> Y , , .
X = C[-2, 4], Y = C[-2, 4], F(x) = .
: , .
.. , .. , , .. ε
, => ≤ ε.
.. , .