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daijiantao

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[求助] 用Matlab化簡(jiǎn)一個(gè)復(fù)雜含參積分式的函數(shù)表達(dá)式已有1人參與

急需化簡(jiǎn)一個(gè)復(fù)雜含參積分的表達(dá)式，表達(dá)式如上傳圖片所示：

由于積分式比較復(fù)雜，之前用matlab做了數(shù)值解，并驗(yàn)證正確了
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)

由于數(shù)值解分別計(jì)算一個(gè)一個(gè)案例非常麻煩，所以想要尋求一下圖片所示公式的化簡(jiǎn)公式，并可以用于Excel等軟件中批量處理。

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daijiantao: 金幣+20, ★★★★★最佳答案, 非常感謝！ 2016-04-11 21:34:58

引用回帖:

6樓: Originally posted by daijiantao at 2016-04-10 23:15:42
如果我只有積分上限變化（tH），其余都不變，能基于上面的程序幫忙給一個(gè)程序嗎，最好可以出圖？...

以下代碼是積分上限tH從100開(kāi)始以間隔1變化到600的例子，可自行根據(jù)實(shí)際修改。
需注意以下代碼為m文件格式，請(qǐng)新建一個(gè)m文件，把以下代碼完整復(fù)制進(jìn)去，再運(yùn)行。

CODE:

function qiu_jifen

clear all;clc

format long

tH_0=100;    %積分上限tH的最小值

tH_n=500;    %積分上限tH的最大值

num=tH_n-tH_0+1;     %積分上限tH總的變化數(shù)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);

計(jì)算結(jié)果：
積分上限tH       數(shù)值積分結(jié)果
ans =

  1.0e+002 *

1.000000000000000  -0.000062764008049
1.010000000000000  -0.000062774137557
1.020000000000000  -0.000062783623116
1.030000000000000  -0.000062792482273
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1.050000000000000  -0.000062808388605
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1.070000000000000  -0.000062821985394
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1.520000000000000  -0.000062709522699
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2.820000000000000  -0.000060801923485
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3.440000000000000  -0.000059718770860
3.450000000000000  -0.000059701242881
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3.470000000000000  -0.000059666192174
3.480000000000000  -0.000059648669685
3.490000000000000  -0.000059631149296
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3.520000000000000  -0.000059578601860
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3.580000000000000  -0.000059473579278
3.590000000000000  -0.000059456086193
3.600000000000000  -0.000059438596446
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3.620000000000000  -0.000059403627380
3.630000000000000  -0.000059386148265
3.640000000000000  -0.000059368672895
3.650000000000000  -0.000059351201369
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3.800000000000000  -0.000059089652104
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3.820000000000000  -0.000059054861786
3.830000000000000  -0.000059037474662
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3.890000000000000  -0.000058933268983
3.900000000000000  -0.000058915921537
3.910000000000000  -0.000058898580034
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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
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4.230000000000000  -0.000058347140439
4.240000000000000  -0.000058330026565
4.250000000000000  -0.000058312920387
4.260000000000000  -0.000058295821944
4.270000000000000  -0.000058278731274
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4.290000000000000  -0.000058244573400
4.300000000000000  -0.000058227506271
4.310000000000000  -0.000058210447061
4.320000000000000  -0.000058193395805
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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
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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

用Matlab化簡(jiǎn)一個(gè)復(fù)雜含參積分式的函數(shù)表達(dá)式-1

附圖1.png

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8樓2016-04-11 10:00:43

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“數(shù)值解分別計(jì)算一個(gè)一個(gè)案例”，對(duì)于不同的案例，積分式什么參數(shù)會(huì)改變？

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2樓2016-04-07 13:51:21

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引用回帖:

2樓: Originally posted by 月只藍(lán) at 2016-04-07 13:51:21
“數(shù)值解分別計(jì)算一個(gè)一個(gè)案例”，對(duì)于不同的案例，積分式什么參數(shù)會(huì)改變？

M N exp n wf0 tH會(huì)變。所以想找一個(gè)含參的近似方程，怎樣用MATLAB實(shí)現(xiàn)呢~

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3樓2016-04-07 23:45:21

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用mathmetica試試吧

發(fā)自小木蟲(chóng)Android客戶(hù)端

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【答案】應(yīng)助回帖

感謝參與，應(yīng)助指數(shù) +1

引用回帖:

3樓: Originally posted by daijiantao at 2016-04-07 23:45:21
M N exp n wf0 tH會(huì)變。所以想找一個(gè)含參的近似方程，怎樣用MATLAB實(shí)現(xiàn)呢~...

M N exp n wf0 tH會(huì)變，寫(xiě)個(gè)循環(huán)語(yǔ)句就解決了。
原積分式即便近似為一個(gè)代數(shù)式，M N exp n wf0 tH會(huì)變的情況下，一樣麻煩。

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5樓2016-04-08 09:30:09

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5樓: Originally posted by 月只藍(lán) at 2016-04-08 09:30:09
M N exp n wf0 tH會(huì)變，寫(xiě)個(gè)循環(huán)語(yǔ)句就解決了。
原積分式即便近似為一個(gè)代數(shù)式，M N exp n wf0 tH會(huì)變的情況下，一樣麻煩。...

如果我只有積分上限變化（tH），其余都不變，能基于上面的程序幫忙給一個(gè)程序嗎，最好可以出圖？

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6樓2016-04-10 23:15:42

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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)

結(jié)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樓2016-04-10 23:56:06

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8樓: Originally posted by 月只藍(lán) at 2016-04-11 10:00:43
以下代碼是積分上限tH從100開(kāi)始以間隔1變化到600的例子，可自行根據(jù)實(shí)際修改。
需注意以下代碼為m文件格式，請(qǐng)新建一個(gè)m文件，把以下代碼完整復(fù)制進(jìn)去，再運(yùn)行。

function qiu_jifen
clear all;clc
format l ...

非常感謝

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9樓2016-04-11 21:59:05

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