18Â¥: Originally posted by zrhcc at 2016-01-12 14:56:36
ÄúºÃ£¬¹ØÓÚ½âµÄ¸öÊý¡£¡£¡£¡£¡£ÎÒͼÖеÄÊǵ缫Ñô¼«µÄÇé¿ö£¬sigma´ú±íµçºÉÃܶȣ¬ËùÒÔΪ¸º£¬¡£¡£¡£ÔÚÒõ¼«£¬¦Ò,d,sÊýÖµÓëÑô¼«Ò»Ñù£¬µ«ÊÇ·ûºÅÏà·´£¬¼´¦Ò,d,sÓÐÁ½¸ö½â£¬µ«ÊÇʣϵÄÁ½¸öÖµcºÍmiu¶¼Ö»ÓÐÒ»¸ö½â¡£...

eqlst = {¦Ò*96485 == (170000000 + 20*¦Ò^2)*s*8314/1000*298/96485,
   ¦Ò == -2*5*Exp[¦Ì]*Sinh[d],
   c == 2*5*Exp[¦Ì]*Cosh[d],
   12/10 == 2*8314/1000*298/96485*Abs[d + s],
   200 == ¦Ì*c};
(*ËäÈ»ºóÐø²»»áÓõ½µ«ÊÇÎÒÒÀ¾É·ÅÕâÀïÁË£¬ÕâÊÇ¿ÉÒÔ·ÖÎö³öÀ´µÄÏÞÖÆÌõ¼þ£º*)
con = {c > 0, ¦Ò < 0, s < 0, 0 < ¦Ì < ProductLog[20], d > 0};
(*SolveÔÚÇó½â³¬Ô½·½³Ìʱ¾­³£ÓÐÀ§ÄÑ£¬ÄÇôÏȾ¡Á¿ÏûÈ¥Ò×ÏûµÄ±äÁ¿¡£*)
neweqlst = List @@ Eliminate[eqlst, {¦Ò, s(*,¦Ì,d*), c}](*//Simplify*)
(*{(-1210681647011250000000000 + 2217483639235220000000 d^2) ¦Ì Cosh[d] ==
  Sinh[d] (19604908166986645000000 d - 1596869827860870015625 E^¦Ì Sinh[d] -
     1043521712581280000 d^2 E^¦Ì Sinh[d] +
     230645978435137000 d E^(2 ¦Ì) Sinh[d]^2 +
     3351367881000000 E^(3 ¦Ì) Sinh[d]^3 - 6138363015184 d^2 E^(3 ¦Ì) Sinh[d]^3),

E^¦Ì ¦Ì Cosh[d] ==
  20,

-19604908166986645000000 d E^¦Ì Sinh[
     d] + (1596869827860870015625 + 1043521712581280000 d^2) E^(2 ¦Ì) Sinh[d]^2 -
   230645978435137000 d E^(3 ¦Ì)
     Sinh[d]^3 + (-3351367881000000 + 6138363015184 d^2) E^(4 ¦Ì) Sinh[d]^4 ==
  24213632940225000000000000 - 44349672784704400000000 d^2}
*)
(*¾ªÑȵط¢ÏÖÎå¸ö·½³ÌÏûÈý¸ö±äÁ¿ºó¾ÓÈ»»¹Ê£Èý¸ö·½³Ì£¬ÆäÖÐÓÐÒ»¸öÌرð¼òµ¥¡£°ÑËüÌá³öÀ´Çó½â£º*)
sold = Solve[{d > 0, neweqlst[[2]]}, d, Reals][[1]]
(*{d -> ConditionalExpression[ArcCosh[(20 E^-¦Ì)/¦Ì], 0 < ¦Ì < ProductLog[20]]}
*)
(*ÓÚÊÇ»ñµÃÁËÒ»¸öµ¥±äÁ¿³¬Ô½·½³Ì¡£²»¹ýÕâ¸ö³¬Ô½·½³ÌFindFit´¦ÀíÆðÀ´ÒÉËÆÓÐÀ§ÄÑ£¨ÎÒÒ²²»Ïë¼ÌÐøÊÔÁË£©ËùÒÔÕâÀïÔÙ¶Èת»»³ÉÇó×îСֵµÄÎÊÌ⣺*)
{$, nsol¦Ì} =
NMinimize[{Subtract @@ neweqlst[[3]]^2 /. d -> sold[[1, -1, 1]],
   sold[[1, -1, -1]]}, ¦Ì, WorkingPrecision -> 16]
(*{0, {¦Ì -> 0.1079199021290265}}
*)
nsold = sold /. sol¦Ì
(* {d -> 5.807316493056165} *)
eqlst /. nsold /. nsol¦Ì
{Rule @@ %[[2]], Rule @@ %[[3]]}
(*{¦Ò -> -1853.192811634474, c -> 1853.226291485000}*)
%% /. %
Solve[%[[1]]]
(*{{s -> -29.17333774289270}}*)
%% /. % // Flatten

5Â¥: Originally posted by zrhcc at 2016-01-11 22:23:28
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2Â¥: Originally posted by zho123855 at 2016-01-11 12:30:57
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2Â¥: Originally posted by zho123855 at 2016-01-11 12:30:57
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3Â¥: Originally posted by zho123855 at 2016-01-11 12:32:19
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6Â¥: Originally posted by dingd at 2016-01-12 10:12:27
1stOptÇó½â£º

sigma: 7.47555409301912E-15
s: 1.65229570538605E-16
mu: -268392899709.37
d: -23.3660212498365
c: -7.45176195855294E-10

5Â¥: Originally posted by zrhcc at 2016-01-11 22:23:28
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9Â¥: Originally posted by zho123855 at 2016-01-12 13:41:34
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