       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.