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MathGroup Archive 2005

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Math5.0 frustrated Compatibility Problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg56932] Math5.0 frustrated Compatibility Problem
  • From: "Jingming Yao" <jingming_yao at hotmail.com>
  • Date: Tue, 10 May 2005 03:42:48 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hello Everyone
  There is a very interesting problem. I have a 4 equations 4 knowns 
nonlinear algebra equation system. It CAN be solved by Math 4.1 or 4.2 but 
it can NOT be solved by Math 5.0. It is the same program. And the error 
message in Math 5.0 is "FindRoot:: jsing: Encountered a singular Jacobian at
the point {p02n, ?¢Vb2n, n02n, JCn, ?Àn}={2.9*10^18, 0.61, 3.7*10^11, 0.5}. 
Try perturbing the initial point(s)." My program is as follows.

u2 = d0 - ((Cb*(
      zVb2 - ?¢Vb2n))/(q*Ns02) + q*Lz*(p02n)/(q*Ns02) + (&#1013;/d)*(z?³s + 
?¢?³sn)/(q*
            Ns02));

u4 = JBp - Jpe0*((p02n/zp02)*
          Exp[-?¢?³sn/VT] - 1) - Jpb0*((
                  p02n/zp02)*Exp[(?¢Vb2n)/VT] - 1) - Jrc0*(?ã(p02n/
    zp02)*Exp[-?¢?³sn/(2*VT)] -
        1) - Jrb0*(?ã(p02n/zp02)*Exp[(?¢Vb2n)/(2*VT)] - 1) - 
q*A*Lz*p02n*n02n;

u6 = ?¢?³sn - (1 - ?¢Vb2n);

u12 = n02n*q*Vn*Exp[-?³emc2/VT] + n02n*q*Vn*Exp[-?³eme2/VT] +
        q*A*Lz*p02n*n02n + (n02n*p02n/(n02n + p02n))*(q*Lz)/?ÑNR - (?Ánc*
            Jnc0*(Exp[(?¢Vb2n)/VT] - 1) + ?Áne*Jne0*(Exp[-?¢?³sn/VT] - 1));

JBp = 0.001;

Answer[i] = FindRoot[{u2, u4, u6, u12}, {p02n, 2.9*10^18}, {?¢Vb2n, 0.61}, {
    n02n, 3.7*10^11}, {?¢?³sn, 0.5}]

The starting values I use above are close to answers Math 4.1 gives me. All 
the others are constants with values like

d0 = 8*10^-7;
d = 5*10^-5;
&#1013; = 13.1*8.854*10^-14;
db = 2.5*10^-6;
Cb = &#1013;/db;
zVb2 = 0.843;
q = 1.60218*10^-19;
Ns02 = 3.2*10^18;
Lz = 6*10^-7;
Jpe0 = 6.29*10^-19;
zp02 = 4*10^9;
z?³s = 0.806;
VT = 0.0259;
Jpb0 = 1.6*10^-29;
Jrc0 = 1.065*10^-10;
Jrb0 = 5.33*10^-12;
A = 10^-10;
Vn = 10^7;
?³emc2 = 0.43;
?³eme2 = 0.446;
?ÑNR = 10^-9;
?Ánc = 0.001;
?Áne = 0.001;
Jnc0 = 2.57*10^-10;
Jne0 = 2.57*10^-10;
?³sn = z?³s + ?¢?³sn;

Anybody has some idea? Thnaks a lot.

Jingming
Uconn, ECE Dept.
Graduate Assistance

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