ЧМ ЛР7
.docx
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')
