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Shirley89

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[求助] 求解微分方程 已有1人参与

使用1stopt软件或者matlab软件计算都行。
方程:
已知t,c求a,b,d,f
-dc/dt=(a*c^2-b*0.25*(9.404-c)^2)/(d*c+0.5*f*(9.404-c)+1)^2
t       c
0        8.769713879
3        5.909461709
6        5.736047766
9        4.756936544
12        4.505799773
15        4.354160734
18        4.124025932
21        3.994725485
31        3.732949397
41        3.680613046
51        3.537445782
61        3.283577643
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月只蓝

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Shirley89: 金币+10, ★有帮助 2015-05-19 21:32:07
我这里计算的结果不稳定,给出几组结果作参考:
第一组:
Correlation Coef. (R): 0.986304176273208
R-Square: 0.972795928133971
Determination Coef. (DC): 0.972792656014291
F-Statistic: 71.7687426318881
Parameters Best Estimate
-------------------- -------------
a 0.00559215260838134
b 0.00662125172153037
d -0.0638103180849573
f 0.0992242074773484
====== Output Results =====
File: Data file - 1
No. Obs. c Cal. c
1 5.909461709 6.0464769024458
2 5.736047766 5.34858078481853
3 4.756936544 4.90534203968303
4 4.505799773 4.59275477547173
5 4.354160734 4.35943704941531
6 4.124025932 4.178964093185


7 3.994725485 4.03592170787528
8 3.732949397 3.72572617575052
9 3.680613046 3.55726512074916
10 3.537445782 3.46037640348784
11 3.283577643 3.40294588283877

第二组:
Correlation Coef. (R): 0.986304176273398
R-Square: 0.972795928134345
Determination Coef. (DC): 0.972792656014291
F-Statistic: 71.7687426318881
Parameters Best Estimate
-------------------- -------------
a 139.787768133856
b 165.512292823622
d 6.61745036314971
f 49.1001612906352
====== Output Results =====
File: Data file - 1
No Obs. c Cal. c
1 5.909461709 6.04647690186977
2 5.736047766 5.34858078472968
3 4.756936544 4.90534203980537
4 4.505799773 4.59275477569249
5 4.354160734 4.35943704967707
6 4.124025932 4.17896409345519
7 3.994725485 4.03592170813435
8 3.732949397 3.7257261759082
9 3.680613046 3.55726512078219
10 3.537445782 3.46037640340734
11 3.283577643 3.40294588266502

第三组:
Correlation Coef. (R): 0.986304176273328
R-Square: 0.972795928134207
Determination Coef. (DC): 0.972792656014291
F-Statistic: 71.7687426318881
Parameters Best Estimate
-------------------- -------------
a 0.0172502054731701
b 0.0204246844974723
d -0.031645302096899
f 0.335125184608859
====== Output Results =====
File: Data file - 1
No Obs. c Cal. c
1 5.909461709 6.04647690226843
2 5.736047766 5.34858078465058
3 4.756936544 4.90534203952475
4 4.505799773 4.5927547753238
5 4.354160734 4.35943704927803
6 4.124025932 4.17896409305837
7 3.994725485 4.03592170775909
8 3.732949397 3.72572617566634
9 3.680613046 3.55726512069123
10 3.537445782 3.46037640345054
11 3.283577643 3.40294588281716

此外,原微分方程可求得解析,可直接作非线性方程拟合,见附图。
求解微分方程
附图2.png

MATLAB、MS小问题、普通问题请发帖求助!时间精力有限,恕不接受无偿私信求助。
2楼2015-05-19 20:08:03
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Shirley89

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引用回帖:
2楼: Originally posted by 月只蓝 at 2015-05-19 20:08:03
我这里计算的结果不稳定,给出几组结果作参考:
第一组:
Correlation Coef. (R): 0.986304176273208
R-Square: 0.972795928133971
Determination Coef. (DC): 0.972792656014291
F-Statistic: 71.76874263188 ...

谢谢啊!可这个解析解是不是太复杂了啊?
3楼2015-05-19 21:34:19
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Shirley89

银虫 (小有名气)

引用回帖:
2楼: Originally posted by 月只蓝 at 2015-05-19 20:08:03
我这里计算的结果不稳定,给出几组结果作参考:
第一组:
Correlation Coef. (R): 0.986304176273208
R-Square: 0.972795928133971
Determination Coef. (DC): 0.972792656014291
F-Statistic: 71.76874263188 ...

您好!您能帮我在拟合三组数据吗?程序是一样的,我想看一下拟合的参数差的多吗。

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4楼2015-05-19 21:45:44
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