. :
b i , r . r - .
y 1, y 2,¼, yr. y 1 , ; y 2 , , .. , y 1, y 2,¼, yr, . y 1, y 2,¼, yr, , .
7
10-5 [0, 1] (0) = 0.
( ), . , .
k | |||
x ' = cos(at + x) + k (t x) | 1.00 | 0.50 | |
-"- | 1.25 | 0.75 | |
-"- | 1.50 | 1.00 | |
-"- | 1.75 | 1.25 | |
-"- | 2.00 | 1.50 | |
x ' = 1 sin(at + x) + | 1.00 | - 0.3 | |
-"- | 1.25 | - 0.1 | |
-"- | 1.50 | 0.1 | |
-"- | 1.75 | 0.3 | |
-"- | 2.00 | 0.5 | |
x ' = + k x 2 | 1.00 | - 0.5 | |
-"- | 1.25 | - 0.3 | |
-"- | 1.50 | - 0.1 | |
-"- | 1.75 | 0.1 | |
-"- | 2.00 | 0.3 | |
x ' = 1 + (a t)sin(x) (k + t) x | 0.50 | 1.00 | |
-"- | 0.75 | 1.25 | |
-"- | 1.00 | 1.50 | |
-"- | 1.25 | 1.75 | |
-"- | 1.50 | 2.00 | |
x ' = (a x 2)cos(t) + k x | 0.6 | 0.2 | |
-"- | 0.7 | 0.3 | |
-"- | 0.8 | 0.4 | |
-"- | 0.9 | 0.5 | |
-"- | 1.0 | 0.6 |
a | k | ||
x ' = 1 + a x sin(t) k x 2 | 0.2 | 1.00 | |
-"- | 0.4 | 1.25 | |
-"- | 0.6 | 1.50 | |
-"- | 0.8 | 1.75 | |
-"- | 1.0 | 2.00 | |
x ' = a e (a + t x) + k (t 2 + x) | 0.2 | 0.3 | |
-"- | 0.4 | 0.4 | |
-"- | 0.6 | 0.5 | |
-"- | 0.8 | 0.6 | |
-"- | 1.0 | 0.7 | |
x ' = | 0.1 | 0.1 | |
-"- | 0.2 | 0.2 | |
-"- | 0.3 | 0.3 | |
-"- | 0.4 | 0.4 | |
-"- | 0.5 | 0.5 | |
x ' = 0.2 ch(a t + x) + | 0.3 | 1.00 | |
-"- | 0.4 | 1.25 | |
-"- | 0.5 | 1.50 | |
-"- | 0.6 | 1.75 | |
-"- | 0.7 | 2.00 | |
- 0.5 | 0.2 | ||
-"- | - 0.4 | 0.3 | |
-"- | - 0.3 | 0.4 | |
-"- | - 0.2 | 0.5 | |
-"- | - 0.1 | 0.6 |
1. Maple :
|
|
h = 0.05 .
2. Mathcad .
"" ( ) . rkfixed ( - ) .
0 0
0.05000000000000 0.00084520959923
0.10000000000000 0.00343083039397
0.15000000000000 0.00783786372686
0.20000000000000 0.01415598922061
0.25000000000000 0.02248458081565
0.30000000000000 0.03293379527424
0.35000000000000 0.04562590720360
0.40000000000000 0.06069676562373
0.45000000000000 0.07829758606469
0.50000000000000 0.09859694045094
0.55000000000000 0.12178321860328
0.60000000000000 0.14806740950846
0.65000000000000 0.17768656848628
0.70000000000000 0.21090780566410
0.75000000000000 0.24803330959979
0.80000000000000 0.28940623751877
0.85000000000000 0.33541823340112
0.90000000000000 0.38651842970525
0.95000000000000 0.44322513172968
1.00000000000000 0.50614014425799
MATLAB
Maple Mathcad
.
3. MATLAB m-:
function df=DifEq(t,x)
global a k
df=(exp(k*x+t)-exp(-(k*x+t)))/(2.0*(0.9+a))+k*x;
:
. .