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SAYRG

½ð³æ (СÓÐÃûÆø)

[ÇóÖú] ʹÓÃFindRoot½âµÃx iÖ®áᣬÈçºÎÕ{ÓÃx i×ö„eµÄß\Ë㣿

????????Mathematica????FindRoot??? x i (x1(i))???????{?? x i (x1(i))?M?????????m???\??
?????????????N??x i (x1(i))?c??????????§Ô??????¨©I?????????????????????
???¦Ò?????}????????????
Input?cOutput??????????¡¤??????o????ám?
Mathematica?????|??????????????????P???

???m??????\???????
CODE:
P1(i)=P(i)*y1/x1(i)
P2(i)=P(i)*y2/x2(i)
N1(i)=a1*b1*P1(i)^c1/(1+b1*P1(i)^c1)+q1*k1*P1(i)^t1/(1+k1*P1(i)^t1)
N2(i)=a2*b2*P2(i)^c2/(1+b2*P2(i)^c2)+q2*k2*P2(i)^t2/(1+k2*P2(i)^t2)
N1(i)=N1(i)*N2(i)/(N2(i)+N1(i)*(1.0/x1(i)-1.0))
N2(i)=N1(i)*(1.0/x1(i)-1.0)
S(i)=P2(i)/P1(i)

?????o???????????????????????????????????N???F??
CODE:
    P(kPa)    S           N1        N2         x1        y1        x2        y2
     5.000    27.825     0.225     0.008     0.965     0.500     0.035     0.500
    10.000    31.437     0.498     0.016     0.969     0.500     0.031     0.500
    15.000    33.984     0.790     0.023     0.971     0.500     0.029     0.500
    20.000    36.056     1.093     0.030     0.973     0.500     0.027     0.500
    25.000    37.855     1.403     0.037     0.974     0.500     0.026     0.500
    50.000    45.016     2.981     0.066     0.978     0.500     0.022     0.500
    75.000    50.876     4.527     0.089     0.981     0.500     0.019     0.500
   100.000    56.171     5.994     0.107     0.983     0.500     0.017     0.500
   125.000    61.116     7.367     0.121     0.984     0.500     0.016     0.500
   250.000    82.906    12.878     0.155     0.988     0.500     0.012     0.500
   375.000   101.913    16.658     0.163     0.990     0.500     0.010     0.500
   500.000   119.429    19.339     0.162     0.992     0.500     0.008     0.500
   625.000   136.015    21.316     0.157     0.993     0.500     0.007     0.500
   750.000   152.054    22.823     0.150     0.993     0.500     0.007     0.500
   875.000   167.663    24.006     0.143     0.994     0.500     0.006     0.500
  1000.000   182.993    24.957     0.136     0.995     0.500     0.005     0.500
  1125.000   198.084    25.736     0.130     0.995     0.500     0.005     0.500
  1500.000   242.459    27.408     0.113     0.996     0.500     0.004     0.500
  1625.000   257.079    27.816     0.108     0.996     0.500     0.004     0.500
  1750.000   271.428    28.173     0.104     0.996     0.500     0.004     0.500
  1999.000   300.055    28.766     0.096     0.997     0.500     0.003     0.500

Input?????
CODE:
lhs=Integrate[((a1*b1*(y1*p/x)^c1)/(1+b1*(y1*p/x)^c1)+(q1*k1*(y1*p/x)^t1)/(1+k1*(y1*p/x)^t1))/p, p]
rhs=Integrate[((a2*b2*(y2*p/(1-x))^c2)/(1+b2*(y2*p/(1-x))^c2)+(q2*k2*(y2*p/(1-x))^t2)/(1+k2*(y2*p/(1 - x))^t2))/p, p]
parameters={a1->32.129608, b1->2.320748*10^-3, c1->1/0.852663, q1->4.372886, k1->1.054925*10^-3, t1->1/1.433036, a2->12.763072, b2->9.155722*10^-5, c2->1/1.034267, q2->4.341261, k2->4.302906*10^-4, t2->1/1.004052, y1->0.5, y2->0.5}
newlhs = lhs /. parameters
newrhs = rhs /. parameters
Grid[Table[FindRoot[newlhs == newrhs, {x, 0.999999999}], {p, 1, 2000, 100}]]

Output?t??D???


[ Last edited by SAYRG on 2012-11-28 at 19:02 ]
»Ø¸´´ËÂ¥

» ²ÂÄãϲ»¶

ÒÑÔÄ   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

walk1997

½ð³æ (ÖøÃûдÊÖ)

¡ï ¡ï ¡ï ¡ï ¡ï ¡ï
jjdg: ½ð±Ò+1, ¸Ðл²ÎÓë 2012-11-30 13:17:31
jjdg: ±à¼­ÄÚÈÝ 2012-11-30 13:17
xzhdty: ½ð±Ò+5, Â¥Ö÷¸øÄãµÄ 2013-01-04 17:07:55
ÄãÕâÀïµÄP£¬x2,y1,y2µÃ×Ô¼ºÊäÈë°É£¬Ôõô²úÉúµÄ£¬ÏÂÃæÀý×Ó Ëæ±ã²úÉúÒ»¸öP,x2, Êä³ö¿ÉÒÔ×Ô¼ºÃÀ»¯ÏÂ
CODE:
Clear["Global`*"];
lhs = Integrate[((a1*b1*(y1*p/x)^c1)/(1 + b1*(y1*p/x)^c1) + (q1*
         k1*(y1*p/x)^t1)/(1 + k1*(y1*p/x)^t1))/p, p];
rhs = Integrate[((a2*b2*(y2*p/(1 - x))^c2)/(1 +
         b2*(y2*p/(1 - x))^c2) + (q2*k2*(y2*p/(1 - x))^t2)/(1 +
         k2*(y2*p/(1 - x))^t2))/p, p];
parameters = {a1 -> 32.129608, b1 -> 2.320748*10^-3, c1 -> 1/0.852663,
    q1 -> 4.372886, k1 -> 1.054925*10^-3, t1 -> 1/1.433036,
   a2 -> 12.763072, b2 -> 9.155722*10^-5, c2 -> 1/1.034267,
   q2 -> 4.341261, k2 -> 4.302906*10^-4, t2 -> 1/1.004052, y1 -> 0.5,
   y2 -> 0.5};
newlhs = lhs /. parameters;
newrhs = rhs /. parameters;
x = x /. Table[
   FindRoot[newlhs == newrhs, {x, 0.999999999}], {p, 1, 2000, 100}]
P = Table[5 i, {i, 1, Length[x]}] // N;
x2 = Table[1, {i, 1, Length[x]}] // N;
y1 = Table[1/2, {i, 1, Length[x]}] // N;
y2 = y1;
x1 = x;
P1 = P*y1/x1;
P2 = P*y2/x2;
N1 = a1*b1*P1^c1/(1 + b1*P1^c1) + q1*k1*P1^t1/(1 + k1*P1^t1) /.
   parameters;
N2 = a2*b2*P2^c2/(1 + b2*P2^c2) + q2*k2*P2^t2/(1 + k2*P2^t2) /.
   parameters;
N1 = N1*N2/(N2 + N1*(1.0/x1 - 1.0));
N2 = N1*(1.0/x1 - 1.0);
S = P2/P1 // N;
Grid[Transpose[{P, S, N1, N2, x1, y1, x2, y2}]]

[ Last edited by jjdg on 2012-11-30 at 13:17 ]

» ±¾ÌûÒÑ»ñµÃµÄºì»¨£¨×îÐÂ10¶ä£©

2Â¥2012-11-30 09:17:12
ÒÑÔÄ   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

SAYRG

½ð³æ (СÓÐÃûÆø)

¡¾´ð°¸¡¿Ó¦Öú»ØÌû

ËÍÏÊ»¨Ò»¶ä
xzhdty: ½ð±Ò+5, лл²ÎÓë 2013-01-04 17:05:35
xzhdty: ½ð±Ò+5, ³ÌÐòÇ¿Ìû-1, ¸ø´íÁË 2013-01-04 17:07:37
xzhdty: ½ð±Ò-10, ³ÌÐòÇ¿Ìû+1, ÓÖ·¢´íÁË 2013-01-04 17:09:47
ÒýÓûØÌû:
2Â¥: Originally posted by walk1997 at 2012-11-30 09:17:12
ÄãÕâÀïµÄP£¬x2,y1,y2µÃ×Ô¼ºÊäÈë°É£¬Ôõô²úÉúµÄ£¬ÏÂÃæÀý×Ó Ëæ±ã²úÉúÒ»¸öP,x2, Êä³ö¿ÉÒÔ×Ô¼ºÃÀ»¯ÏÂ

Clear;
lhs = Integrate;
rhs = Integrate;
parameters = {a1 -> 32.129608, b1 -> 2.320748*10^-3, c1 ...

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Œ‘ß@‚€³ÌÐòµÄÄ¿µÄÖ÷ÒªÊÇÒªÇóµÃ²»Í¬‰ºÁ¦•rµÄx£¬Ò²¾ÍÊÇx1¡£
¶øx1+x2=1, y1+y2=1¡£ËùÒÔÖ»ÒªÇóµÃx£¬ÄÇx2 = 1-x ÁË¡£

Ö»ÓЉºÁ¦P, y1, y2 ÒÔ¼°ÆäËû…¢”µ(Èça1, b1, c1......µÈ)ÐèÒªÊÂÏÈÝ”Èë¡£

x = x /. Table[
   FindRoot[newlhs == newrhs, {x, 0.999999999}], {p, 1, 2000, 100}]
3Â¥2012-11-30 15:01:35
ÒÑÔÄ   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû
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