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小木虫论坛-学术科研互动平台 » 计算模拟区 » 程序语言 » MATLAB/Mathematica » 用Matlab化简一个复杂含参积分式的函数表达式
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daijiantao

新虫 (正式写手)

[求助] 用Matlab化简一个复杂含参积分式的函数表达式已有1人参与

急需化简一个复杂含参积分的表达式，表达式如上传图片所示：
用Matlab化简一个复杂含参积分式的函数表达式

由于积分式比较复杂，之前用matlab做了数值解，并验证正确了
format long
clc,clear
M=0.230873094;
N=0.025914445;
n=0.86;
exp=114.8;
wf0=46;
tH=300;
F = @(t,p1,p2,p3,p4,p5)(((p1./(1+t)-p2.*log10(1+t)./(1+t)).^p3./p4)-(p1./(1+t)-p2.*log10(1+t)./(1+t))./p5);
dc=quadl(@(x)F(x,M,N,n,exp,wf0),0,tH)

由于数值解分别计算一个一个案例非常麻烦，所以想要寻求一下图片所示公式的化简公式，并可以用于Excel等软件中批量处理。
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1楼2016-04-07 09:52:28
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月只蓝

主管区长 (职业作家)
“数值解分别计算一个一个案例”，对于不同的案例，积分式什么参数会改变？
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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2016-04-07 13:51:21
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daijiantao

新虫 (正式写手)
引用回帖:
2楼: Originally posted by 月只蓝 at 2016-04-07 13:51:21
“数值解分别计算一个一个案例”，对于不同的案例，积分式什么参数会改变？

M N exp n wf0 tH会变。所以想找一个含参的近似方程，怎样用MATLAB实现呢~
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3楼2016-04-07 23:45:21
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wyyacgh

铁杆木虫 (职业作家)
用mathmetica试试吧

发自小木虫Android客户端
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彪悍的人生，不需要签名！
4楼2016-04-08 07:21:45
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月只蓝

主管区长 (职业作家)

【答案】应助回帖

感谢参与，应助指数 +1
引用回帖:
3楼: Originally posted by daijiantao at 2016-04-07 23:45:21
M N exp n wf0 tH会变。所以想找一个含参的近似方程，怎样用MATLAB实现呢~...

M N exp n wf0 tH会变，写个循环语句就解决了。
原积分式即便近似为一个代数式，M N exp n wf0 tH会变的情况下，一样麻烦。
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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。
5楼2016-04-08 09:30:09
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daijiantao

新虫 (正式写手)
引用回帖:
5楼: Originally posted by 月只蓝 at 2016-04-08 09:30:09
M N exp n wf0 tH会变，写个循环语句就解决了。
原积分式即便近似为一个代数式，M N exp n wf0 tH会变的情况下，一样麻烦。...

如果我只有积分上限变化（tH），其余都不变，能基于上面的程序帮忙给一个程序吗，最好可以出图？
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6楼2016-04-10 23:15:42
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ybkooo

至尊木虫 (著名写手)

^^
syms p1 p2 p3 p4 p5 tH t
F = (((p1./(1+t)-p2.*log10(1+t)./(1+t)).^p3./p4)-(p1./(1+t)-p2.*log10(1+t)./(1+t))./p5);
ff=int(F,t,0,tH);
latex(ff)

结果(不咋的)：
ans =

\int _{0}^{{\it tH}}\! \left( {\frac {{\it p1}}{1+t}}-{\frac {{\it p2}\,\ln  \left( 1+t \right) }{\ln  \left( 10 \right)  \left( 1+t \right) }} \right) ^{{\it p3}}{{\it p4}}^{-1}- \left( {\frac {{\it p1}}{1+t}}-{\frac {{\it p2}\,\ln  \left( 1+t \right) }{\ln  \left( 10 \right)  \left( 1+t \right) }} \right) {{\it p5}}^{-1}{dt}
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abcd
7楼2016-04-10 23:56:06
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月只蓝

主管区长 (职业作家)

【答案】应助回帖

★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★
daijiantao: 金币+20, ★★★★★最佳答案, 非常感谢！ 2016-04-11 21:34:58
引用回帖:
6楼: Originally posted by daijiantao at 2016-04-10 23:15:42
如果我只有积分上限变化（tH），其余都不变，能基于上面的程序帮忙给一个程序吗，最好可以出图？...

以下代码是积分上限tH从100开始以间隔1变化到600的例子，可自行根据实际修改。
需注意以下代码为m文件格式，请新建一个m文件，把以下代码完整复制进去，再运行。
CODE:
function qiu_jifen
clear all;clc
format long
tH_0=100;    %积分上限tH的最小值
tH_n=500;    %积分上限tH的最大值
num=tH_n-tH_0+1;     %积分上限tH总的变化数目

tH_data=linspace(tH_0,tH_n,num);
for i=1:length(tH_data)
    tH=tH_data(i);
    dc(i)=quadgk(@obj,0,tH);
end
[tH_data' dc']
figure(1)
plot(tH_data,dc,'b-')

function f=obj(t)
M=0.230873094;
N=0.025914445;
n=0.86;
exp=114.8;
wf0=46;
p1=M;
p2=N;
p3=n;
p4=exp;
p5=wf0;
f=(((p1./(1+t)-p2.*log10(1+t)./(1+t)).^p3./p4)-(p1./(1+t)-p2.*log10(1+t)./(1+t))./p5);

计算结果：
积分上限tH          数值积分结果
ans =

  1.0e+002 *

   1.000000000000000  -0.000062764008049
   1.010000000000000  -0.000062774137557
   1.020000000000000  -0.000062783623116
   1.030000000000000  -0.000062792482273
   1.040000000000000  -0.000062800731978
   1.050000000000000  -0.000062808388605
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   1.070000000000000  -0.000062821985394
   1.080000000000000  -0.000062827955645
   1.090000000000000  -0.000062833393040
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   1.110000000000000  -0.000062842724180
   1.120000000000000  -0.000062846644291
   1.130000000000000  -0.000062850084306
   1.140000000000000  -0.000062853056388
   1.150000000000000  -0.000062855572318
   1.160000000000000  -0.000062857643510
   1.170000000000000  -0.000062859281030
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   1.200000000000000  -0.000062861697206
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   1.460000000000000  -0.000062757833934
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   1.500000000000000  -0.000062726429213
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   1.570000000000000  -0.000062664009028
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   1.620000000000000  -0.000062614230524
   1.630000000000000  -0.000062603801121
   1.640000000000000  -0.000062593221338
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   1.660000000000000  -0.000062571622857
   1.670000000000000  -0.000062560610099
   1.680000000000000  -0.000062549458846
   1.690000000000000  -0.000062538171902
   1.700000000000000  -0.000062526752009
   1.710000000000000  -0.000062515201849
   1.720000000000000  -0.000062503524043
   1.730000000000000  -0.000062491721154
   1.740000000000000  -0.000062479795691
   1.750000000000000  -0.000062467750106
   1.760000000000000  -0.000062455586798
   1.770000000000000  -0.000062443308113
   1.780000000000000  -0.000062430916348
   1.790000000000000  -0.000062418413750
   1.800000000000000  -0.000062405802518
   1.810000000000000  -0.000062393084803
   1.820000000000000  -0.000062380262713
   1.830000000000000  -0.000062367338308
   1.840000000000000  -0.000062354313608
   1.850000000000000  -0.000062341190589
   1.860000000000000  -0.000062327971185
   1.870000000000000  -0.000062314657291
   1.880000000000000  -0.000062301250763
   1.890000000000000  -0.000062287753418
   1.900000000000000  -0.000062274167037
   1.910000000000000  -0.000062260493362
   1.920000000000000  -0.000062246734103
   1.930000000000000  -0.000062232890932
   1.940000000000000  -0.000062218965490
   1.950000000000000  -0.000062204959383
   1.960000000000000  -0.000062190874186
   1.970000000000000  -0.000062176711442
   1.980000000000000  -0.000062162472664
   1.990000000000000  -0.000062148159335
   2.000000000000000  -0.000062133772907
   2.010000000000000  -0.000062119314805
   2.020000000000000  -0.000062104786427
   2.030000000000000  -0.000062090189141
   2.040000000000000  -0.000062075524292
   2.050000000000000  -0.000062060793195
   2.060000000000000  -0.000062045997143
   2.070000000000000  -0.000062031137402
   2.080000000000000  -0.000062016215215
   2.090000000000000  -0.000062001231800
   2.100000000000000  -0.000061986188353
   2.110000000000000  -0.000061971086047
   2.120000000000000  -0.000061955926033
   2.130000000000000  -0.000061940709439
   2.140000000000000  -0.000061925437374
   2.150000000000000  -0.000061910110925
   2.160000000000000  -0.000061894731159
   2.170000000000000  -0.000061879299122
   2.180000000000000  -0.000061863815843
   2.190000000000000  -0.000061848282330
   2.200000000000000  -0.000061832699574
   2.210000000000000  -0.000061817068546
   2.220000000000000  -0.000061801390200
   2.230000000000000  -0.000061785665474
   2.240000000000000  -0.000061769895287
   2.250000000000000  -0.000061754080542
   2.260000000000000  -0.000061738222127
   2.270000000000000  -0.000061722320913
   2.280000000000000  -0.000061706377753
   2.290000000000000  -0.000061690393489
   2.300000000000000  -0.000061674368946
   2.310000000000000  -0.000061658304934
   2.320000000000000  -0.000061642202248
   2.330000000000000  -0.000061626061671
   2.340000000000000  -0.000061609883971
   2.350000000000000  -0.000061593669902
   2.360000000000000  -0.000061577420206
   2.370000000000000  -0.000061561135611
   2.380000000000000  -0.000061544816832
   2.390000000000000  -0.000061528464574
   2.400000000000000  -0.000061512079528
   2.410000000000000  -0.000061495662371
   2.420000000000000  -0.000061479213772
   2.430000000000000  -0.000061462734387
   2.440000000000000  -0.000061446224861
   2.450000000000000  -0.000061429685826
   2.460000000000000  -0.000061413117907
   2.470000000000000  -0.000061396521714
   2.480000000000000  -0.000061379897851
   2.490000000000000  -0.000061363246909
   2.500000000000000  -0.000061346569469
   2.510000000000000  -0.000061329866103
   2.520000000000000  -0.000061313137374
   2.530000000000000  -0.000061296383834
   2.540000000000000  -0.000061279606028
   2.550000000000000  -0.000061262804489
   2.560000000000000  -0.000061245979743
   2.570000000000000  -0.000061229132307
   2.580000000000000  -0.000061212262690
   2.590000000000000  -0.000061195371392
   2.600000000000000  -0.000061178458903
   2.610000000000000  -0.000061161525708
   2.620000000000000  -0.000061144572283
   2.630000000000000  -0.000061127599095
   2.640000000000000  -0.000061110606605
   2.650000000000000  -0.000061093595265
   2.660000000000000  -0.000061076565521
   2.670000000000000  -0.000061059517811
   2.680000000000000  -0.000061042452565
   2.690000000000000  -0.000061025370208
   2.700000000000000  -0.000061008271158
   2.710000000000000  -0.000060991155824
   2.720000000000000  -0.000060974024611
   2.730000000000000  -0.000060956877916
   2.740000000000000  -0.000060939716130
   2.750000000000000  -0.000060922539637
   2.760000000000000  -0.000060905348818
   2.770000000000000  -0.000060888144043
   2.780000000000000  -0.000060870925681
   2.790000000000000  -0.000060853694091
   2.800000000000000  -0.000060836449630
   2.810000000000000  -0.000060819192646
   2.820000000000000  -0.000060801923485
   2.830000000000000  -0.000060784642484
   2.840000000000000  -0.000060767349976
   2.850000000000000  -0.000060750046291
   2.860000000000000  -0.000060732731750
   2.870000000000000  -0.000060715406673
   2.880000000000000  -0.000060698071372
   2.890000000000000  -0.000060680726154
   2.900000000000000  -0.000060663371324
   2.910000000000000  -0.000060646007180
   2.920000000000000  -0.000060628634016
   2.930000000000000  -0.000060611252121
   2.940000000000000  -0.000060593861780
   2.950000000000000  -0.000060576463274
   2.960000000000000  -0.000060559056880
   2.970000000000000  -0.000060541642868
   2.980000000000000  -0.000060524221507
   2.990000000000000  -0.000060506793061
   3.000000000000000  -0.000060489357789
   3.010000000000000  -0.000060471915947
   3.020000000000000  -0.000060454467787
   3.030000000000000  -0.000060437013556
   3.040000000000000  -0.000060419553500
   3.050000000000000  -0.000060402087857
   3.060000000000000  -0.000060384616865
   3.070000000000000  -0.000060367140758
   3.080000000000000  -0.000060349659765
   3.090000000000000  -0.000060332174111
   3.100000000000000  -0.000060314684021
   3.110000000000000  -0.000060297189713
   3.120000000000000  -0.000060279691403
   3.130000000000000  -0.000060262189304
   3.140000000000000  -0.000060244683626
   3.150000000000000  -0.000060227174576
   3.160000000000000  -0.000060209662356
   3.170000000000000  -0.000060192147167
   3.180000000000000  -0.000060174629206
   3.190000000000000  -0.000060157108668
   3.200000000000000  -0.000060139585745
   3.210000000000000  -0.000060122060624
   3.220000000000000  -0.000060104533491
   3.230000000000000  -0.000060087004530
   3.240000000000000  -0.000060069473922
   3.250000000000000  -0.000060051941842
   3.260000000000000  -0.000060034408467
   3.270000000000000  -0.000060016873969
   3.280000000000000  -0.000059999338517
   3.290000000000000  -0.000059981802279
   3.300000000000000  -0.000059964265420
   3.310000000000000  -0.000059946728102
   3.320000000000000  -0.000059929190484
   3.330000000000000  -0.000059911652725
   3.340000000000000  -0.000059894114980
   3.350000000000000  -0.000059876577402
   3.360000000000000  -0.000059859040141
   3.370000000000000  -0.000059841503346
   3.380000000000000  -0.000059823967175
   3.390000000000000  -0.000059806431749
   3.400000000000000  -0.000059788897221
   3.410000000000000  -0.000059771363731
   3.420000000000000  -0.000059753831418
   3.430000000000000  -0.000059736300416
   3.440000000000000  -0.000059718770860
   3.450000000000000  -0.000059701242881
   3.460000000000000  -0.000059683716610
   3.470000000000000  -0.000059666192174
   3.480000000000000  -0.000059648669685
   3.490000000000000  -0.000059631149296
   3.500000000000000  -0.000059613631116
   3.510000000000000  -0.000059596115264
   3.520000000000000  -0.000059578601860
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用Matlab化简一个复杂含参积分式的函数表达式-1
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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。
8楼2016-04-11 10:00:43
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daijiantao

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8楼: Originally posted by 月只蓝 at 2016-04-11 10:00:43
以下代码是积分上限tH从100开始以间隔1变化到600的例子，可自行根据实际修改。
需注意以下代码为m文件格式，请新建一个m文件，把以下代码完整复制进去，再运行。

function qiu_jifen
clear all;clc
format l ...

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9楼2016-04-11 21:59:05
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