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Добавлен: 01.08.2019
Просмотров: 224
Скачиваний: 1
x = 0:0.01:1;
y(1) = 1;
h = x(2)-x(1);
for i = 1:1:length(x)-1
y(i+1) = y(i)+h*x(i)^2;
end
y1 = x.^3/3+1;
e = abs(y-y1)
e = 0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0002 0.0002 0.0002 0.0002 0.0002 0.0003 0.0003 0.0003 0.0003 0.0004 0.0004 0.0004 0.0004 0.0005 0.0005 0.0005 0.0006 0.0006 0.0006 0.0007 0.0007 0.0008 0.0008 0.0008 0.0009 0.0009 0.0010 0.0010 0.0011 0.0011 0.0011 0.0012 0.0012 0.0013 0.0013 0.0014 0.0014 0.0015 0.0016 0.0016 0.0017 0.0017 0.0018 0.0019 0.0019 0.0020 0.0020 0.0021 0.0022 0.0022 0.0023 0.0024 0.0024 0.0025 0.0026 0.0027 0.0027 0.0028 0.0029 0.0030 0.0030 0.0031 0.0032 0.0033 0.0033 0.0034 0.0035 0.0036 0.0037 0.0038 0.0039 0.0039 0.0040 0.0041 0.0042 0.0043 0.0044 0.0045 0.0046 0.0047 0.0048 0.0049 0.0050
Аналитически:
>> test
T =
0
0.0000
0.0000
0.0000
0.0000
0.0000
0.0001
0.0001
0.0001
0.0002
0.0004
0.0005
0.0006
0.0013
0.0019
0.0025
0.0031
0.0063
0.0094
0.0126
0.0157
0.0314
0.0471
0.0628
0.0785
0.1440
0.2096
0.2751
0.3406
0.4056
0.4705
0.5354
0.6003
0.6628
0.7252
0.7877
0.8502
0.9136
0.9770
1.0405
1.1039
1.1633
1.2226
1.2819
1.3413
1.4032
1.4651
1.5270
1.5888
1.6453
1.7017
1.7582
1.8146
1.8793
1.9439
2.0085
2.0732
2.1344
2.1957
2.2569
2.3182
2.3917
2.4653
2.5388
2.6124
2.6843
2.7563
2.8282
2.9002
2.9694
3.0386
3.1078
3.1770
3.2462
3.3154
3.3847
3.4539
3.5184
3.5829
3.6474
3.7119
3.7643
3.8167
3.8691
3.9215
3.9816
4.0418
4.1020
4.1622
4.2368
4.3114
4.3860
4.4606
4.5311
4.6016
4.6721
4.7426
4.8131
4.8836
4.9541
5.0245
5.0870
5.1494
5.2118
5.2742
5.3377
5.4011
5.4646
5.5280
5.6082
5.6884
5.7685
5.8487
5.9467
6.0447
6.1427
6.2407
6.3503
6.4599
6.5695
6.6791
6.7874
6.8957
7.0040
7.1124
7.2134
7.3145
7.4155
7.5166
7.6008
7.6850
7.7693
7.8535
7.9270
8.0004
8.0739
8.1474
8.2092
8.2711
8.3329
8.3948
8.4627
8.5307
8.5987
8.6667
8.7449
8.8231
8.9013
8.9795
9.0668
9.1542
9.2416
9.3289
9.4290
9.5290
9.6290
9.7290
9.8311
9.9333
10.0355
10.1376
10.2393
10.3410
10.4427
10.5444
10.6304
10.7163
10.8022
10.8881
10.9645
11.0409
11.1172
11.1936
11.2600
11.3265
11.3929
11.4594
11.5234
11.5874
11.6514
11.7154
11.7908
11.8662
11.9416
12.0171
12.1011
12.1851
12.2691
12.3531
12.4476
12.5422
12.6368
12.7314
12.8395
12.9476
13.0558
13.1639
13.2695
13.3752
13.4808
13.5865
13.6755
13.7646
13.8537
13.9428
14.0215
14.1001
14.1788
14.2575
14.3269
14.3964
14.4658
14.5353
14.5950
14.6548
14.7145
14.7743
14.8307
14.8871
14.9436
15.0000
Y =
1.0000 0
1.0000 -0.0001
1.0000 -0.0001
1.0000 -0.0002
1.0000 -0.0002
1.0000 -0.0005
1.0000 -0.0007
1.0000 -0.0010
1.0000 -0.0012
1.0000 -0.0025
1.0000 -0.0037
1.0000 -0.0050
1.0000 -0.0062
1.0000 -0.0125
1.0000 -0.0188
1.0000 -0.0250
1.0000 -0.0312
0.9998 -0.0623
0.9996 -0.0932
0.9992 -0.1239
0.9988 -0.1543
0.9952 -0.3033
0.9893 -0.4467
0.9812 -0.5843
0.9710 -0.7161
0.9075 -1.1995
0.8160 -1.5715
0.7040 -1.8304
0.5787 -1.9802
0.4479 -2.0285
0.3170 -1.9874
0.1915 -1.8698
0.0758 -1.6895
-0.0231 -1.4703
-0.1073 -1.2203
-0.1752 -0.9527
-0.2261 -0.6791
-0.2605 -0.4059
-0.2779 -0.1478
-0.2797 0.0870
-0.2675 0.2924
-0.2452 0.4542
-0.2142 0.5841
-0.1765 0.6812
-0.1341 0.7458
-0.0866 0.7801
-0.0381 0.7830
0.0097 0.7578
0.0552 0.7085
0.0935 0.6461
0.1279 0.5707
0.1577 0.4859
0.1826 0.3951
0.2047 0.2875
0.2198 0.1806
0.2281 0.0782
0.2301 -0.0163
0.2265 -0.0967
0.2184 -0.1663
0.2064 -0.2239
0.1912 -0.2693
0.1699 -0.3076
0.1464 -0.3289
0.1219 -0.3347
0.0975 -0.3271
0.0746 -0.3089
0.0532 -0.2827
0.0340 -0.2509
0.0172 -0.2159
0.0035 -0.1812
-0.0079 -0.1473
-0.0170 -0.1157
-0.0240 -0.0875
-0.0292 -0.0635
-0.0329 -0.0441
-0.0354 -0.0297
-0.0371 -0.0202
-0.0382 -0.0154
-0.0391 -0.0142
-0.0401 -0.0162
-0.0413 -0.0206
-0.0425 -0.0257
-0.0440 -0.0317
-0.0458 -0.0383
-0.0480 -0.0452
-0.0510 -0.0531
-0.0544 -0.0606
-0.0583 -0.0672
-0.0625 -0.0728
-0.0681 -0.0778
-0.0740 -0.0805
-0.0801 -0.0807
-0.0860 -0.0783
-0.0914 -0.0738
-0.0964 -0.0674
-0.1008 -0.0592
-0.1047 -0.0495
-0.1078 -0.0386
-0.1101 -0.0270
-0.1116 -0.0148
-0.1122 -0.0025
-0.1120 0.0084
-0.1112 0.0190
-0.1096 0.0293
-0.1075 0.0390
-0.1047 0.0482
-0.1014 0.0567
-0.0976 0.0645
-0.0932 0.0715
-0.0872 0.0792
-0.0806 0.0857
-0.0735 0.0911
-0.0660 0.0954
-0.0564 0.0995
-0.0465 0.1024
-0.0364 0.1043
-0.0261 0.1054
-0.0145 0.1059
-0.0029 0.1056
0.0086 0.1045
0.0199 0.1028
0.0310 0.1003
0.0417 0.0969
0.0519 0.0926
0.0617 0.0873
0.0702 0.0814
0.0781 0.0745
0.0852 0.0668
0.0915 0.0583
0.0961 0.0506
0.1001 0.0424
0.1033 0.0338
0.1057 0.0249
0.1073 0.0170
0.1082 0.0089
0.1086 0.0007
0.1083 -0.0075
0.1077 -0.0143
0.1066 -0.0211
0.1051 -0.0278
0.1031 -0.0344
0.1005 -0.0414
0.0975 -0.0483
0.0940 -0.0549
0.0900 -0.0612
0.0850 -0.0680
0.0794 -0.0745
0.0734 -0.0804
0.0668 -0.0858
0.0591 -0.0913
0.0509 -0.0960
0.0424 -0.1000
0.0335 -0.1032
0.0230 -0.1060
0.0123 -0.1077
0.0015 -0.1083
-0.0093 -0.1079
-0.0203 -0.1064
-0.0310 -0.1037
-0.0414 -0.1001
-0.0514 -0.0954
-0.0608 -0.0897
-0.0696 -0.0830
-0.0777 -0.0756
-0.0850 -0.0674
-0.0905 -0.0599
-0.0953 -0.0519
-0.0994 -0.0435
-0.1027 -0.0349
-0.1051 -0.0269
-0.1068 -0.0188
-0.1080 -0.0106
-0.1084 -0.0023
-0.1084 0.0049
-0.1078 0.0121
-0.1068 0.0193
-0.1052 0.0263
-0.1033 0.0330
-0.1010 0.0396
-0.0983 0.0459
-0.0951 0.0521
-0.0909 0.0592
-0.0862 0.0659
-0.0810 0.0722
-0.0754 0.0781
-0.0685 0.0841
-0.0612 0.0896
-0.0535 0.0944
-0.0454 0.0985
-0.0359 0.1024
-0.0261 0.1053
-0.0160 0.1073
-0.0058 0.1083
0.0059 0.1083
0.0176 0.1070
0.0290 0.1045
0.0401 0.1007
0.0505 0.0959
0.0604 0.0901
0.0695 0.0832
0.0779 0.0755
0.0843 0.0682
0.0900 0.0605
0.0951 0.0522
0.0993 0.0436
0.1025 0.0356
0.1049 0.0275
0.1068 0.0191
0.1079 0.0107
0.1084 0.0032
0.1084 -0.0044
0.1078 -0.0119
0.1067 -0.0193
0.1054 -0.0257
0.1037 -0.0319
0.1016 -0.0381
0.0991 -0.0441
0.0965 -0.0496
0.0935 -0.0550
0.0903 -0.0602
0.0867 -0.0652
[T1 Y1] = ode45('oscil',[0 15],[1;0]);
[T2 Y2] = ode23('oscil',[0 15],[1;0]);
plot(T1,Y1(:,1))
grid on
hold on
plot(T1,Y1(:,2))
title('ode45')
legend('y1','y2')
figure
plot(T2,Y2(:,1))
grid on
hold on
plot(T2,Y2(:,2))
legend('y1','y2')
title('ode23')
>> t = 0:0.0001:15;
>> y = (exp(-t).*(87*cos(3*t)+26*sin(3*t))+(9*sin(t)-2*cos(t)))/85;
>> dy = (9*cos(t))/85 + (2*sin(t))/85 - (87*cos(3*t) + 26*sin(3*t))./(85*exp(t)) + (78*cos(3*t) - 261*sin(3*t))./(85*exp(t));
>> plot(t,y)
hold on
grid on
>> plot(t,dy)
>> y = [log(0.01) 1/0.01];
>> [T1 Y1] = ode45('oscil',[0.01 5],y)
T1 =
0.0100
0.0105
0.0110
0.0115
0.0120
0.0142
0.0163
0.0185
0.0207
0.0241
0.0274
0.0308
0.0342
0.0399
0.0456
0.0513
0.0569
0.0664
0.0758
0.0852
0.0947
0.1101
0.1255
0.1409
0.1563
0.1808
0.2053
0.2299
0.2544
0.2791
0.3039
0.3286
0.3534
0.3781
0.4029
0.4276
0.4524
0.4771
0.5019
0.5266
0.5514
0.5761
0.6009
0.6256
0.6504
0.6751
0.6999
0.7246
0.7494
0.7741
0.7989
0.8236
0.8484
0.8731
0.8979
0.9226
0.9474
0.9605
0.9737
0.9868
1.0000
Y1 =
-4.6052 100.0000
-4.5562 95.2163
-4.5094 90.8698
-4.4648 86.9028
-4.4221 83.2673
-4.2565 70.5256
-4.1146 61.2076
-3.9904 54.0770
-3.8797 48.4014
-3.7276 41.5547
-3.5957 36.4226
-3.4792 32.4237
-3.3747 29.2018
-3.2213 25.0381
-3.0885 21.9244
-2.9712 19.5024
-2.8662 17.5534
-2.7129 15.0520
-2.5802 13.1808
-2.4631 11.7252
-2.3582 10.5537
-2.2075 9.0725
-2.0768 7.9594
-1.9612 7.0905
-1.8576 6.3894
-1.7120 5.5196
-1.5851 4.8600
-1.4725 4.3415
-1.3713 3.9212
-1.2787 3.5725
-1.1940 3.2809
-1.1159 3.0332
-1.0435 2.8200
-0.9761 2.6348
-0.9129 2.4723
-0.8536 2.3287
-0.7975 2.2008
-0.7445 2.0861
-0.6942 1.9828
-0.6463 1.8891
-0.6006 1.8039
-0.5569 1.7260
-0.5151 1.6545
-0.4750 1.5887
-0.4364 1.5278
-0.3993 1.4715
-0.3636 1.4191
-0.3290 1.3703
-0.2957 1.3247
-0.2634 1.2821
-0.2322 1.2420
-0.2019 1.2044
-0.1726 1.1690
-0.1441 1.1356
-0.1163 1.1040
-0.0894 1.0742
-0.0632 1.0458
-0.0495 1.0314
-0.0360 1.0173
-0.0227 1.0036
-0.0096 0.9903
>> plot(T1,Y1(:,1))
>> hold on
>> grid on
>> plot(T1,Y1(:,2))
>> axis([0 5 -10 10])
>> t = 0.01:0.001:5;
>> Y = log(t);
>> plot(t,Y)
>> plot(t,Y,'--g')
>> Y = 1./t;
>> plot(t,Y,'--y')