数模实验.docx
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数模实验.docx
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数模实验
江西农业大学
数模实验曹丹20123209
一
[x,y]=dsolve('Dx=-a*x','Dy=a*x-b*y','x(0)=1100','y(0)=0')
结果x=1100*exp(-a*t)y=1100/(a-b)*a*exp(-b*t)-1100/(a-b)*a*exp(-a*t)
a=log
(2)/5;b=log
(2)/6;
t=0:
30;
x=1100.*exp(-a.*t)
y=1100./(a-b).*a.*exp(-b.*t)-1100./(a-b).*a.*exp(-a.*t)
plot(t,x,'b',t,y,'r')
结果
y(3)
236.5588
functionmyfun(t)
a=log
(2)/5;b=log
(2)/6;
x=1100.*exp(-a.*t);
y=1100./(a-b).*a.*exp(-b.*t)-1100./(a-b).*a.*exp(-a.*t);
myfun(t)=y-400;
输入x0=3;
t=fsolve(@myfun,x0)
t=4.8648
a1=log
(2)/5;b1=log
(2)/6;b2=2*b1;
t=0:
30;
x=1100.*exp(-a1.*t);
y1=1100./(a1-b1).*a1.*exp(-b1.*t)-1100./(a1-b1).*a1.*exp(-a1.*t);
y2=((1100*a1)./(exp(b1*t).*(a1-b1))-(1100*a1)./(exp(a1*t).*(a1-b1))).*(t<2)+((1100*a1)./(exp(b2*t).*(a1-b2))-(1100*a1)./(exp(a1*t).*(a1-b2))).*(t>=2);
plot(t,x,'b',t,y1,'r',t,y2,'g')
二
Nihe1.m
functiony=nihe1(a,x)
y=a
(1)*exp(a
(2)*x);
a2.m
x=0:
1:
11;
y=[3.9,5.3,7.2,9.6,12.9,17.1,23.2,31.4,38.6,50.2,62.9,76];
a=lsqcurvefit('nihe1',[1,1],x,y)
y1=nihe1(a,x)'
y'
plot(x,y,x,y1,'*')
x=12;
y=a
(1)*exp(a
(2)*x)
结果a=5.29010.2453
Y1=5.2901
6.7608
8.6405
11.0427
14.1127
18.0363
23.0507
29.4592
37.6493
48.1164
61.4936
78.5899
3.9000
5.3000
7.2000
9.6000
12.9000
17.1000
23.2000
31.4000
38.6000
50.2000
62.9000
76.0000
X=12时
100.4392
Nihe2.m
functiony=nihe2(a,x)
y=a
(1)./(1+(((a
(1)./a(3))-1)).*exp(-a
(2).*x));
b2.m
x=0:
1:
11;
y=[3.9,5.3,7.2,9.6,12.9,17.1,23.2,31.4,38.6,50.2,62.9,76];
a=lsqcurvefit('nihe2',[1,1,1],x,y);
a'
y2=nihe2(a,x)'
y'
plot(x,y,x,y2,'*')
结果
164.3067
0.3297
3.6594
Y2=
3.6594
5.0446
6.9315
9.4822
12.8946
17.3971
23.2305
30.6123
39.6800
50.4208
62.6083
75.7815
3.9000
5.3000
7.2000
9.6000
12.9000
17.1000
23.2000
31.4000
38.6000
50.2000
62.9000
76.0000
三
ill.m文件
functiony=ill(t,x)
a=1;b=0.3;
y=[a*x
(1)*x
(2)-b*x
(1),-a*x
(1)*x
(2)]';
illd.m文件
ts=0:
50;
x0=[0.02,0.98];
[t,x]=ode45('ill',ts,x0);[t,x]
plot(t,x(:
1),t,x(:
2)),pause
plot(x(:
2),x(:
1)),grid
结果
00.02000.9800
1.00000.03900.9525
2.00000.07320.9019
3.00000.12850.8169
4.00000.20330.6927
5.00000.27950.5438
6.00000.33120.3995
7.00000.34440.2839
8.00000.32470.2027
9.00000.28630.1493
10.00000.24180.1145
11.00000.19860.0917
12.00000.15990.0767
13.00000.12720.0665
14.00000.10040.0593
15.00000.07870.0543
16.00000.06140.0507
17.00000.04780.0480
18.00000.03710.0460
19.00000.02870.0445
20.00000.02230.0434
21.00000.01720.0426
22.00000.01330.0419
23.00000.01030.0415
24.00000.00790.0411
25.00000.00610.0408
26.00000.00470.0406
27.00000.00360.0404
28.00000.00280.0403
29.00000.00220.0402
30.00000.00170.0401
31.00000.00130.0400
32.00000.00100.0400
33.00000.00080.0400
34.00000.00060.0399
35.00000.00050.0399
36.00000.00040.0399
37.00000.00030.0399
38.00000.00020.0399
39.00000.00020.0399
40.00000.00010.0399
41.00000.00010.0399
42.00000.00010.0399
43.00000.00010.0399
44.00000.00000.0398
45.00000.00000.0398
46.00000.00000.0398
47.00000.00000.0398
48.00000.00000.0398
49.00000.00000.0398
50.00000.00000.0398
Shier.m文件
functiony=shier(t,x)
r=1;d=0.5;a=0.1;b=0.02;
y=[(r-a*x
(2)).*x
(1),(-d+b*x
(1)).*x
(2)]';
Shierd.m文件
ts=0:
0.1:
15;
x0=[25,2];
[t,x]=ode45('shier',ts,x0);
[t,x]
plot(t,x),gtext('x(t)'),gtext('y(t)'),
pause,plot(x(:
2),x(:
1)),grid
结果
025.00002.0000
0.100027.08182.0041
0.200029.33442.0170
0.300031.76892.0394
0.400034.39612.0726
0.500037.22582.1178
0.600040.26732.1767
0.700043.50122.2534
0.800046.93602.3503
0.900050.60722.4683
1.000054.53012.6106
1.100058.69992.7819
1.200063.09172.9891
1.300067.66043.2411
1.400072.34093.5484
1.500077.04793.9238
1.600081.67594.3819
1.700086.09964.9391
1.800090.17325.6140
1.900093.73116.4268
2.000096.58737.4000
2.100098.53608.5577
2.200099.30559.9234
2.300098.614311.5085
2.400096.285113.3067
2.500092.247215.2882
2.600086.585317.3947
2.700079.534919.5427
2.800071.536421.6225
2.900063.084823.5300
3.000054.623625.1819
3.100046.544126.5163
3.200039.186027.4921
3.300032.793228.0978
3.400027.336828.3766
3.500022.737528.3764
3.600018.913428.1426
3.700015.777127.7178
3.800013.235427.1426
3.900011.187326.4556
4.00009.527825.6911
4.10008.175824.8740
4.20007.068424.0245
4.30006.159223.1580
4.40005.418522.2853
4.50004.812921.4162
4.60004.312420.5582
4.70003.896719.7164
4.80003.550018.8948
4.90003.260118.0961
5.00003.018117.3219
5.10002.815416.5735
5.20002.646015.8515
5.30002.504715.1562
5.40002.387214.4875
5.50002.289813.8454
5.60002.209913.2295
5.70002.145512.6393
5.80002.095312.0740
5.90002.057811.5330
6.00002.031711.0154
6.10002.016210.5207
6.20002.010610.0479
6.30002.01439.5964
6.40002.02709.1653
6.50002.04838.7539
6.60002.07818.3614
6.70002.11647.9870
6.80002.16327.6300
6.90002.21887.2897
7.00002.28336.9654
7.10002.35736.6565
7.20002.44106.3622
7.30002.53516.0821
7.40002.64015.8155
7.50002.75665.5618
7.60002.88555.3204
7.70003.02765.0910
7.80003.18374.8729
7.90003.35494.6656
8.00003.54244.4688
8.10003.74784.2819
8.20003.97234.1046
8.30004.21743.9365
8.40004.48473.7773
8.50004.77613.6265
8.60005.09373.4838
8.70005.43983.3490
8.80005.81713.2217
8.90006.22833.1017
9.00006.67662.9888
9.10007.16532.8826
9.20007.69782.7831
9.30008.27812.6900
9.40008.91002.6032
9.50009.59802.5225
9.600010.34682.4479
9.700011.16202.3794
9.800012.04942.3166
9.900013.01532.2596
10.000014.06652.2084
10.100015.21022.1629
10.200016.45412.1233
10.300017.80632.0898
10.400019.27552.0627
10.500020.87082.0422
10.600022.60162.0287
10.700024.47792.0228
10.800026.51022.0249
10.900028.70932.0355
11.000031.08442.0558
11.100033.64162.0875
11.200036.39822.1308
11.300039.36802.1869
11.400042.55982.2573
11.500045.97762.3447
11.600049.62052.4525
11.700053.48292.5849
11.800057.55392.7468
11.900061.81802.9441
12.000066.25493.1834
12.100070.84283.4692
12.200075.52223.8129
12.300080.19004.2348
12.400084.72134.7545
12.500088.96865.3918
12.600092.76226.1658
12.700095.91027.0955
12.800098.19868.1995
12.900099.39109.4962
13.000099.228711.0036
13.100097.436012.7384
13.200093.897214.6791
13.300088.688516.7638
13.400082.012918.9151
13.500074.220421.0377
13.600065.797123.0201
13.700057.254024.7617
13.800049.023826.1948
13.900041.434227.2791
14.000034.706228.0016
14.100028.935128.3802
14.200024.066028.4610
14.300020.010528.2919
14.400016.675927.9181
14.500013.965027.3821
14.600011.774226.7239
14.70009.998225.9788
14.80008.554025.1736
14.90007.376224.3300
15.00006.415823.4645
四
model:
max=72*x1+64*x2;
x1+x2=50;
12*x1+8*x2<480;
3*x1<100;
end
结果
灵敏度分析
model:
sets:
cang/1..3/:
wet,vol;
wu/1..4/:
w,v,p;
link(wu,cang):
x;
endsets
data:
wet=10,16,8;vol=6800,8700,5300;
w=18,15,23,12;v=480,650,580,390;
p=3100,3800,3500,2850;
enddata
max=@sum(wu(i):
p(i)*@sum(cang(j):
x(i,j)));
@for(wu(i):
@sum(cang(j):
x(i,j)) @for(cang(j): @sum(wu(i): x(i,j)) @for(cang(j): @sum(wu(i): v(i)*x(i,j)) @for(cang(j): @for(cang(k)|k#GT#j: @sum(wu(i): x(i,j)/wet(j))=@sum(wu(i): x(i,k)/wet(k))); ); end 结果 model: max=2*x1+3*x2+4*x3; 1.5*x1+3*x2+5*x3<600; 280*x1+250*x2+400*x3<60000; x1*(x1-80)>0; x2*(x2-80)>0; x3*(x3-80)>0; @gin(x1);@gin(x2);@gin(x3); end 结果
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