matlab 等式化简,用Matlab化简一个复杂含参积分式的函数表达式 - 程序语言 - 小木虫 - 学术科研互动社区...

梦里梦外; 2023-01-13 10:15 90阅读 0赞

![cfdc6361174d9cfc8169daed13483a0c.gif][]

月只蓝

“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？

![noavatar.png][]

daijiantao

引用回帖:

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~

![d68c772fe4d681640cb4c64e8f61f157.png][]

wyyacgh

用mathmetica试试吧

![cfdc6361174d9cfc8169daed13483a0c.gif][]

月只蓝

引用回帖:

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。

![noavatar.png][]

daijiantao

引用回帖:

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？

![6569392bbddb676f76f819e41db3bdb3.gif][]

ybkooo

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\}

![cfdc6361174d9cfc8169daed13483a0c.gif][]

月只蓝

引用回帖:

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

1.060000000000000  -0.000062815467978

1.070000000000000  -0.000062821985394

1.080000000000000  -0.000062827955645

1.090000000000000  -0.000062833393040

1.100000000000000  -0.000062838311419

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

1.180000000000000  -0.000062860495604

1.190000000000000  -0.000062861297633

1.200000000000000  -0.000062861697206

1.210000000000000  -0.000062861704109

1.220000000000000  -0.000062861327838

1.230000000000000  -0.000062860577611

1.240000000000000  -0.000062859462376

1.250000000000000  -0.000062857990818

1.260000000000000  -0.000062856171376

1.270000000000000  -0.000062854012244

1.280000000000000  -0.000062851521385

1.290000000000000  -0.000062848706536

1.300000000000000  -0.000062845575217

1.310000000000000  -0.000062842134738

1.320000000000000  -0.000062838392207

1.330000000000000  -0.000062834354535

1.340000000000000  -0.000062830028448

1.350000000000000  -0.000062825420484

1.360000000000000  -0.000062820537008

1.370000000000000  -0.000062815384213

1.380000000000000  -0.000062809968127

1.390000000000000  -0.000062804294619

1.400000000000000  -0.000062798369402

1.410000000000000  -0.000062792198041

1.420000000000000  -0.000062785785954

1.430000000000000  -0.000062779138422

1.440000000000000  -0.000062772260588

1.450000000000000  -0.000062765157464

1.460000000000000  -0.000062757833934

1.470000000000000  -0.000062750294760

1.480000000000000  -0.000062742544584

1.490000000000000  -0.000062734587930

1.500000000000000  -0.000062726429213

1.510000000000000  -0.000062718072737

1.520000000000000  -0.000062709522699

1.530000000000000  -0.000062700783196

1.540000000000000  -0.000062691858225

1.550000000000000  -0.000062682751684

1.560000000000000  -0.000062673467380

1.570000000000000  -0.000062664009028

1.580000000000000  -0.000062654380255

1.590000000000000  -0.000062644584600

1.600000000000000  -0.000062634625523

1.610000000000000  -0.000062624506398

1.620000000000000  -0.000062614230524

1.630000000000000  -0.000062603801121

1.640000000000000  -0.000062593221338

1.650000000000000  -0.000062582494248

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

3.530000000000000  -0.000059561091021

3.540000000000000  -0.000059543582862

3.550000000000000  -0.000059526077497

3.560000000000000  -0.000059508575038

3.570000000000000  -0.000059491075595

3.580000000000000  -0.000059473579278

3.590000000000000  -0.000059456086193

3.600000000000000  -0.000059438596446

3.610000000000000  -0.000059421110141

3.620000000000000  -0.000059403627380

3.630000000000000  -0.000059386148265

3.640000000000000  -0.000059368672895

3.650000000000000  -0.000059351201369

3.660000000000000  -0.000059333733782

3.670000000000000  -0.000059316270230

3.680000000000000  -0.000059298810807

3.690000000000000  -0.000059281355605

3.700000000000000  -0.000059263904715

3.710000000000000  -0.000059246458228

3.720000000000000  -0.000059229016231

3.730000000000000  -0.000059211578812

3.740000000000000  -0.000059194146056

3.750000000000000  -0.000059176718049

3.760000000000000  -0.000059159294872

3.770000000000000  -0.000059141876609

3.780000000000000  -0.000059124463341

3.790000000000000  -0.000059107055146

3.800000000000000  -0.000059089652104

3.810000000000000  -0.000059072254292

3.820000000000000  -0.000059054861786

3.830000000000000  -0.000059037474662

3.840000000000000  -0.000059020092992

3.850000000000000  -0.000059002716850

3.860000000000000  -0.000058985346308

3.870000000000000  -0.000058967981437

3.880000000000000  -0.000058950622305

3.890000000000000  -0.000058933268983

3.900000000000000  -0.000058915921537

3.910000000000000  -0.000058898580034

3.920000000000000  -0.000058881244539

3.930000000000000  -0.000058863915118

3.940000000000000  -0.000058846591834

3.950000000000000  -0.000058829274749

3.960000000000000  -0.000058811963925

3.970000000000000  -0.000058794659424

3.980000000000000  -0.000058777361305

3.990000000000000  -0.000058760069627

4.000000000000000  -0.000058742784448

4.010000000000000  -0.000058725505825

4.020000000000000  -0.000058708233816

4.030000000000000  -0.000058690968475

4.040000000000000  -0.000058673709857

4.050000000000000  -0.000058656458015

4.060000000000000  -0.000058639213004

4.070000000000000  -0.000058621974875

4.080000000000000  -0.000058604743680

4.090000000000000  -0.000058587519469

4.100000000000000  -0.000058570302292

4.110000000000000  -0.000058553092198

4.120000000000000  -0.000058535889236

4.130000000000000  -0.000058518693453

4.140000000000000  -0.000058501504897

4.150000000000000  -0.000058484323612

4.160000000000000  -0.000058467149645

4.170000000000000  -0.000058449983040

4.180000000000000  -0.000058432823842

4.190000000000000  -0.000058415672093

4.200000000000000  -0.000058398527837

4.210000000000000  -0.000058381391115

4.220000000000000  -0.000058364261969

4.230000000000000  -0.000058347140439

4.240000000000000  -0.000058330026565

4.250000000000000  -0.000058312920387

4.260000000000000  -0.000058295821944

4.270000000000000  -0.000058278731274

4.280000000000000  -0.000058261648413

4.290000000000000  -0.000058244573400

4.300000000000000  -0.000058227506271

4.310000000000000  -0.000058210447061

4.320000000000000  -0.000058193395805

4.330000000000000  -0.000058176352538

4.340000000000000  -0.000058159317295

4.350000000000000  -0.000058142290108

4.360000000000000  -0.000058125271011

4.370000000000000  -0.000058108260036

4.380000000000000  -0.000058091257215

4.390000000000000  -0.000058074262579

4.400000000000000  -0.000058057276159

4.410000000000000  -0.000058040297986

4.420000000000000  -0.000058023328089

4.430000000000000  -0.000058006366497

4.440000000000000  -0.000057989413240

4.450000000000000  -0.000057972468345

4.460000000000000  -0.000057955531841

4.470000000000000  -0.000057938603755

4.480000000000000  -0.000057921684114

4.490000000000000  -0.000057904772944

4.500000000000000  -0.000057887870271

4.510000000000000  -0.000057870976121

4.520000000000000  -0.000057854090519

4.530000000000000  -0.000057837213489

4.540000000000000  -0.000057820345056

4.550000000000000  -0.000057803485244

4.560000000000000  -0.000057786634075

4.570000000000000  -0.000057769791574

4.580000000000000  -0.000057752957761

4.590000000000000  -0.000057736132661

4.600000000000000  -0.000057719316293

4.610000000000000  -0.000057702508680

4.620000000000000  -0.000057685709843

4.630000000000000  -0.000057668919801

4.640000000000000  -0.000057652138576

4.650000000000000  -0.000057635366187

4.660000000000000  -0.000057618602654

4.670000000000000  -0.000057601847995

4.680000000000000  -0.000057585102230

4.690000000000000  -0.000057568365376

4.700000000000000  -0.000057551637451

4.710000000000000  -0.000057534918474

4.720000000000000  -0.000057518208462

4.730000000000000  -0.000057501507431

4.740000000000000  -0.000057484815398

4.750000000000000  -0.000057468132379

4.760000000000000  -0.000057451458391

4.770000000000000  -0.000057434793449

4.780000000000000  -0.000057418137569

4.790000000000000  -0.000057401490764

4.800000000000000  -0.000057384853051

4.810000000000000  -0.000057368224444

4.820000000000000  -0.000057351604955

4.830000000000000  -0.000057334994601

4.840000000000000  -0.000057318393393

4.850000000000000  -0.000057301801345

4.860000000000000  -0.000057285218470

4.870000000000000  -0.000057268644781

4.880000000000000  -0.000057252080290

4.890000000000000  -0.000057235525009

4.900000000000000  -0.000057218978950

4.910000000000000  -0.000057202442124

4.920000000000000  -0.000057185914543

4.930000000000000  -0.000057169396217

4.940000000000000  -0.000057152887158

4.950000000000000  -0.000057136387376

4.960000000000000  -0.000057119896881

4.970000000000000  -0.000057103415682

4.980000000000000  -0.000057086943791

4.990000000000000  -0.000057070481216

5.000000000000000  -0.000057054027967

![w134h1122189\_1460340040\_588.png][w134h1122189_1460340040_588.png]

附图1.png

，

[cfdc6361174d9cfc8169daed13483a0c.gif]: /images/20221022/d590751c96244e929edcdcfc8136e79f.png
[noavatar.png]: http://muchongimg.xmcimg.com/data/emuch_bbs_images/app/noavatar.png
[d68c772fe4d681640cb4c64e8f61f157.png]: /images/20221022/7b3970e8637143d3bd34f4a190abf2ad.png
[6569392bbddb676f76f819e41db3bdb3.gif]: /images/20221022/e9d7370cd9b64ce7984ca94cbfbd4458.png
[w134h1122189_1460340040_588.png]: http://muchongimg.xmcimg.com/data/bcs/2016/0411/w134h1122189_1460340040_588.png