compare.m

有限差分法（crank_nicholson finite difference ) 求解色谱模型

figure

expe2=[10,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75;0,0,0.001536983669549,0.001248799231508,0.000480307396734,0,-0.002497598463016,-0.000384245917387,0.000480307396734,0.004226705091258,0.028242074927954,0.10028818443804,0.206916426512968,0.33852065321806,0.424975984630163,0.551777137367915,0.643996157540826,0.728530259365994,0.790009606147935,0.832276657060519,0.878386167146974,0.889913544668588,0.912968299711816,0.939865513928915,0.962920268972142,0.970605187319885,0.966762728146014,0.966762728146014,0.962920268972142,0.970605187319885,0.98597502401537,0.993659942363112,0.98597502401537,0.989817483189241,0.999423631123919,0.993659942363112,0.993659942363112,1.001344860710855,0.98597502401537,0.98597502401537,0.98597502401537,0.98597502401537,0.98597502401537,0.98597502401537,0.98597502401537,0.98597502401537,0.98597502401537,0.98597502401537,0.98597502401537,0.98597502401537,0.98597502401537,0.997502401536984,0.997502401536984,0.997502401536984,0.997502401536984,0.997502401536984,0.997502401536984;]';

cal1=[0	0
0.792234177	0
1.584468354	0
2.376702532	0
3.168936709	8E-15
3.961170886	1.12E-13
4.753405063	1.174E-12
5.545639241	1.0092E-11
6.337873418	7.3246E-11
7.130107595	4.58379E-10
7.922341772	2.51378E-09
8.714575949	1.22376E-08
9.506810127	5.34487E-08
10.2990443	2.11318E-07
11.09127848	7.62151E-07
11.88351266	2.52456E-06
12.67574684	7.72674E-06
13.46798101	2.19708E-05
14.26021519	5.83334E-05
15.05244937	0.000145289
15.84468354	0.000340949
16.63691772	0.000756951
17.4291519	0.001596094
18.22138608	0.003208211
19.01362025	0.006168801
19.80585443	0.011384377
20.59808861	0.0202275
21.39032278	0.034702728
22.18255696	0.057642122
22.97479114	0.092924249
23.76702532	0.145702314
24.55925949	0.222612333
25.35149367	0.331908286
26.14372785	0.483436184
26.93596203	0.688316586
27.7281962	0.958170884
28.52043038	1.303736597
29.31266456	1.732827802
30.10489873	2.247860227
30.89713291	2.843551258
31.68936709	3.505734256
32.48160127	4.212161621
33.27383544	4.935498244
34.06606962	5.647687818
34.8583038	6.324203566
35.65053797	6.946875479
36.44277215	7.504811493
37.23500633	7.993750656
38.02724051	8.414561577
38.81947468	8.771541458
39.61170886	9.070919621
40.40394304	9.319726087
41.19617722	9.525030072
41.98841139	9.693482251
42.78064557	9.831077668
43.57287975	9.943065122
44.36511392	10.03394617
45.1573481	10.10752399
45.94958228	10.16697618
46.74181646	10.21493549
47.53405063	10.25356928
48.32628481	10.28465295
49.11851899	10.30963518
49.91075316	10.32969434
50.70298734	10.34578655
51.49522152	10.358686
52.2874557	10.36901844
53.07968987	10.37728892
53.87192405	10.38390457
54.66415823	10.38919316
55.45639241	10.39341836
56.24862658	10.39679203
57.04086076	10.39948429
57.83309494	10.40163161
58.62532911	10.40334342
59.41756329	10.40470734
60.20979747	10.40579356
61.00203165	10.40665821
61.79426582	10.40734617
62.5865	10.4078933
];
cal2=[0	0
0.632186869	0
1.264373737	0
1.896560606	0
2.528747475	0
3.160934343	0
3.793121212	0
4.425308081	0
5.057494949	0
5.689681818	0
6.321868687	2E-15
6.954055556	1.4E-14
7.586242424	8.3E-14
8.218429293	4.5E-13
8.850616162	2.239E-12
9.48280303	1.0254E-11
10.1149899	4.3489E-11
10.74717677	1.71637E-10
11.37936364	6.3321E-10
12.01155051	2.19258E-09
12.64373737	7.15256E-09
13.27592424	2.20585E-08
13.90811111	6.45221E-08
14.54029798	1.79552E-07
15.17248485	4.76734E-07
15.80467172	1.21107E-06
16.43685859	2.95127E-06
17.06904545	6.91675E-06
17.70123232	1.5628E-05
18.33341919	3.41219E-05
18.96560606	7.21568E-05
19.59779293	0.00014811
20.2299798	0.000295716
20.86216667	0.00057548
21.49435354	0.001093705
22.1265404	0.002033754
22.75872727	0.003706797
23.39091414	0.006633309
24.02310101	0.011672619
24.65528788	0.020226575
25.28747475	0.034555359
25.91966162	0.058257682
26.55184848	0.096978775
27.18403535	0.15940083
27.81622222	0.258498875
28.44840909	0.412818969
29.08059596	0.647010558
29.71278283	0.98994946
30.3449697	1.468046463
30.97715657	2.092753079
31.60934343	2.847346911
32.2415303	3.684950684
32.87371717	4.54409642
33.50590404	5.370358374
34.13809091	6.128213232
34.77027778	6.800909691
35.40246465	7.384982644
36.03465152	7.88465349
36.66683838	8.307853117
37.29902525	8.663820481
37.93121212	8.96179298
38.56339899	9.210360383
39.19558586	9.417194725
39.82777273	9.588983014
40.4599596	9.731463056
41.09214646	9.849506946
41.72433333	9.947221987
42.3565202	10.02805321
42.98870707	10.09487961
43.62089394	10.15010074
44.25308081	10.19571259
44.88526768	10.23337293
45.51745455	10.26445709
46.14964141	10.29010498
46.78182828	10.31126076
47.41401515	10.32870596
48.04620202	10.34308719
48.67838889	10.35493919
49.31057576	10.364704
49.94276263	10.37274693
50.57494949	10.37936978
51.20713636	10.38482176
51.83932323	10.38930865
52.4715101	10.39300028
53.10369697	10.39603678
53.73588384	10.39853374
54.36807071	10.40058649
55.00025758	10.4022736
55.63244444	10.40365985
56.26463131	10.40479859
56.89681818	10.40573378
57.52900505	10.40650161
58.16119192	10.40713188
58.79337879	10.40764911
59.42556566	10.40807347
60.05775253	10.40842156
60.68993939	10.40870701
61.32212626	10.40894105
61.95431313	10.4091329
62.5865	10.40929012
];
cal3=[0	0
1.27727551	1E-15
2.55455102	3.2E-14
3.831826531	7.55E-13
5.109102041	1.156E-11
6.386377551	1.30956E-10
7.663653061	1.17234E-09
8.940928571	8.64745E-09
10.21820408	5.41213E-08
11.49547959	2.93797E-07
12.7727551	1.40755E-06
14.05003061	6.03701E-06
15.32730612	2.34644E-05
16.60458163	8.35379E-05
17.88185714	0.000275069
19.15913265	0.000845192
20.43640816	0.002443616
21.71368367	0.006699671
22.99095918	0.017544197
24.26823469	0.044158068
25.5455102	0.107339406
26.82278571	0.252457356
28.10006122	0.57224276
29.37733673	1.23123866
30.65461224	2.431109097
31.93188776	4.184692987
33.20916327	6.056749316
34.48643878	7.544820277
35.76371429	8.568242854
37.0409898	9.236996164
38.31826531	9.665099787
39.59554082	9.937637025
40.87281633	10.11042164
42.15009184	10.22011148
43.42736735	10.28958349
44.70464286	10.33370304
45.98191837	10.3616386
47.25919388	10.37938399
48.53646939	10.39061084
49.8137449	10.39774047
51.09102041	10.40224488
52.36829592	10.40510359
53.64557143	10.4069065
54.92284694	10.4080498
56.20012245	10.40876941
57.47739796	10.40922539
58.75467347	10.40951178
60.03194898	10.40969315
61.30922449	10.4098068
62.5865	10.40987874
];

plot(expe2(:,1),expe2(:,2)*10.41,'ko',cal1(:,1),cal1(:,2),'k',cal2(:,1),cal2(:,2),'r',cal3(:,1),cal3(:,2),'g');hold on;
store2=[cal(:,1),cal(:,2)*10.41];
xlabel('Time (min)');ylabel('concentration (g/100mL)')
legend('experimental','langmuir','modified langmuir','Bi-langmuir',4)
Title('10.41g/100mL');
box on