- m m
(7.18)
(7.19)
(7.18), (7.19) - . m (x 0, X) (7.18), x 0 (7.19). , [ x 0, X ] N
l - yl (x) xi +1 -
(7.20)
yl , i yl (x) xi.
(7.20). Kl , i
K 1,1, K 2,1, , Km ,1,
K 1,2, K 2,2, , Km ,2,
K 1,3, K 2,3, , Km ,3,
K 1,4, K 2,4, , Km ,4,
y 1, i +1, y 2, i +1,, ym , i +1.
7.4. [1, 2]
Excel. .
[1, 2] N = 10 . h = 0,1.
m = 3. Kl , i 12. fl (x, y 1, y 2, y 3) Kl , i:
Function f_1(ByVal x, ByVal y_1, ByVal y_2, ByVal y_3)
f_1 = 2 * x * y_1 / y_2
End Function
Function f_2(ByVal x, ByVal y_1, ByVal y_2, ByVal y_3)
f_2 = 8 * y_3 / (3 * y_2)
End Function
Function f_3(ByVal x, ByVal y_1, ByVal y_2, ByVal y_3)
f_3 = 3 * y_3 / y_1
End Function
Function K_1_1(ByVal x, ByVal y_1, ByVal y_2, ByVal y_3)
K_1_1 = f_1(x, y_1, y_2, y_3)
End Function
Function K_2_1(ByVal x, ByVal y_1, ByVal y_2, ByVal y_3)
K_2_1 = f_2(x, y_1, y_2, y_3)
End Function
Function K_3_1(ByVal x, ByVal y_1, ByVal y_2, ByVal y_3)
K_3_1 = f_3(x, y_1, y_2, y_3)
End Function
Function K_1_2(ByVal x, ByVal y_1, ByVal y_2, ByVal y_3, ByVal h)
K11 = K_1_1(x, y_1, y_2, y_3)
K21 = K_2_1(x, y_1, y_2, y_3)
K31 = K_3_1(x, y_1, y_2, y_3)
K_1_2 = f_1(x + h / 2, y_1 + h * K11 / 2, y_2 + h * K21 / 2, y_3 + h * K31 / 2)
End Function
Function K_2_2(ByVal x, ByVal y_1, ByVal y_2, ByVal y_3, ByVal h)
K11 = K_1_1(x, y_1, y_2, y_3)
K21 = K_2_1(x, y_1, y_2, y_3)
K31 = K_3_1(x, y_1, y_2, y_3)
K_2_2 = f_2(x + h / 2, y_1 + h * K11 / 2, y_2 + h * K21 / 2, y_3 + h * K31 / 2)
End Function
Function K_3_2(ByVal x, ByVal y_1, ByVal y_2, ByVal y_3, ByVal h)
K11 = K_1_1(x, y_1, y_2, y_3)
K21 = K_2_1(x, y_1, y_2, y_3)
K31 = K_3_1(x, y_1, y_2, y_3)
K_3_2 = f_3(x + h / 2, y_1 + h * K11 / 2, y_2 + h * K21 / 2, y_3 + h * K31 / 2)
End Function
Function K_1_3(ByVal x, ByVal y_1, ByVal y_2, ByVal y_3, ByVal h)
K12 = K_1_2(x, y_1, y_2, y_3, h)
K22 = K_2_2(x, y_1, y_2, y_3, h)
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|
K32 = K_3_2(x, y_1, y_2, y_3, h)
K_1_3 = f_1(x + h / 2, y_1 + h * K12 / 2, y_2 + h * K22 / 2, y_3 + h * K32 / 2)
End Function
Function K_2_3(ByVal x, ByVal y_1, ByVal y_2, ByVal y_3, ByVal h)
K12 = K_1_2(x, y_1, y_2, y_3, h)
K22 = K_2_2(x, y_1, y_2, y_3, h)
K32 = K_3_2(x, y_1, y_2, y_3, h)
K_2_3 = f_2(x + h / 2, y_1 + h * K12 / 2, y_2 + h * K22 / 2, y_3 + h * K32 / 2)
End Function
Function K_3_3(ByVal x, ByVal y_1, ByVal y_2, ByVal y_3, ByVal h)
K12 = K_1_2(x, y_1, y_2, y_3, h)
K22 = K_2_2(x, y_1, y_2, y_3, h)
K32 = K_3_2(x, y_1, y_2, y_3, h)
K_3_3 = f_3(x + h / 2, y_1 + h * K12 / 2, y_2 + h * K22 / 2, y_3 + h * K32 / 2)
End Function
Function K_1_4(ByVal x, ByVal y_1, ByVal y_2, ByVal y_3, ByVal h)
K13 = K_1_3(x, y_1, y_2, y_3, h)
K23 = K_2_3(x, y_1, y_2, y_3, h)
K33 = K_3_3(x, y_1, y_2, y_3, h)
K_1_4 = f_1(x + h, y_1 + h * K13, y_2 + h * K23, y_3 + h * K33)
End Function
Function K_2_4(ByVal x, ByVal y_1, ByVal y_2, ByVal y_3, ByVal h)
K13 = K_1_3(x, y_1, y_2, y_3, h)
K23 = K_2_3(x, y_1, y_2, y_3, h)
K33 = K_3_3(x, y_1, y_2, y_3, h)
K_2_4 = f_2(x + h, y_1 + h * K13, y_2 + h * K23, y_3 + h * K33)
End Function
Function K_3_4(ByVal x, ByVal y_1, ByVal y_2, ByVal y_3, ByVal h)
K13 = K_1_3(x, y_1, y_2, y_3, h)
K23 = K_2_3(x, y_1, y_2, y_3, h)
K33 = K_3_3(x, y_1, y_2, y_3, h)
K_3_4 = f_3(x + h, y_1 + h * K13, y_2 + h * K23, y_3 + h * K33)
End Function
Excel. Visual Basic Insert Module .
Excel , 7.9. 1 2 A . B 3, C 3 D 3 .
B 1 h. 13 (. 7.8):
7.8
B4 | =B3+h*(K_1_1(A3;B3;C3;D3)+2*K_1_2(A3;B3;C3;D3;h) +2*K_1_3(A3;B3;C3;D3;h)+K_1_4(A3;B3;C3;D3;h))/6 |
C4 | =C3+h*(K_2_1(A3;B3;C3;D3)+2*K_2_2(A3;B3;C3;D3;h) +2*K_2_3(A3;B3;C3;D3;h)+K_2_4(A3;B3;C3;D3;h))/6 |
D4 | =D3+h*(K_3_1(A3;B3;C3;D3)+2*K_3_2(A3;B3;C3;D3;h) +2*K_3_3(A3;B3;C3;D3;h)+K_3_4(A3;B3;C3;D3;h))/6 |
E3 | =A3 |
F3 | =2*A3^2 |
G3 | =3*A3^3 |
B, C D y 1, y 2, y 3.
7.9
A | B | C | D | E | F | G | |||
1 | h= | 0,1 |
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| ||||
2 | xi | y1i | y2i | y3i | y1=x | y2=2x^2 | y3=3x^3 | ||
3 | 1 | 1 | 2 | 3 | 1 | 2 | 3 | ||
4 | 1,1 | 1,100004 | 2,419978 | 3,992938 | 1,1 | 2,42 | 3,993 | ||
5 | 1,2 | 1,200008 | 2,879958 | 5,183862 | 1,2 | 2,88 | 5,184 | ||
6 | 1,3 | 1,300012 | 3,379938 | 6,590769 | 1,3 | 3,38 | 6,591 | ||
7 | 1,4 | 1,400016 | 3,919918 | 8,231656 | 1,4 | 3,92 | 8,232 | ||
8 | 1,5 | 1,50002 | 4,499897 | 10,12452 | 1,5 | 4,5 | 10,125 | ||
9 | 1,6 | 1,600025 | 5,119874 | 12,28735 | 1,6 | 5,12 | 12,288 | ||
10 | 1,7 | 1,700029 | 5,779848 | 14,73815 | 1,7 | 5,78 | 14,739 | ||
11 | 1,8 | 1,800034 | 6,479821 | 17,49492 | 1,8 | 6,48 | 17,496 | ||
12 | 1,9
| 1,90004 | 7,21979 | 20,57564 | 1,9 | 7,22 | 20,577 | ||
13 | 2 | 2,000045 | 7,999757 | 23,99832 | 2 | 8 | 24 |
, .