Solvin differential equation.....

[sohiltri]

close all;
clear all;

vact=0.8427e-16; %active volume of laser cavity
gco=8.0e-11; %gain constant
Nctr=0.59e23; %transparency electron density
tn=3e-9; %spontaneous recombination lifetime
tp=0.7e-12; %photon lifetime
beeta=1e-3; %fraction of spontaneous emission coupled into lasing mode
gamma=0.4; %optical confinement factor
epsilon=2.0e-23; %gain compression fator
Nm=9; %number of side modes
lambdaocw=1.3e-6; %max gain wave length
k=.083e-9; %wavelength change per degree kelvin
dellambda=8; %gain line width
n=2; %ideality factor
Rs=5.6; %effective series diode resistance
Tol=30; %leakage current characteristic temp
Cleak=2.27e-6; %leakage current proportionality constant
Toa=100; %active region charcterstic temp
Rther=100; %effective thermal diode resistance
q=1.6e-19;
lambdai=1310e-9;
Tcw=300; %reference temp
Nc=4.35e23; %intrinsic carrier density gallium arsenide
Nv=7.57e18;
h=1.05457e-34; %planks constant
c=3e8; %velocity of light

Ntr='Nctr*exp(-T/Toa)';

NcT='Nc*(T/300)^1.5';

NvT='Nv*(T/300)^1.5';

Eg='1.519-(5.405e-4*T^2)/(T+204)';

Ne='((NcT*NvT)^0.5)*exp(-Eg/(2*k*T))';
Ne=subs(Ne,'NvT',NvT);
Ne=subs(Ne,'NcT',NcT);
Ne=subs(Ne,'Eg',Eg);

Tdin='Td-T+Rther*Rs*(q*vact*N/tn)^2+(n*k*Td*vact*N/tn)*log((N/Ne)+1)';
[Td]=solve(Tdin,'Td');


goi='gco*exp(-T/Toa)*(1-4*((lambdai-(lambdaocw+k*(Td-Tcw)))/dellambda)^2)';
goi=subs(goi,'Td',Td(1));

Sin='goi/(1+epsilon*S)*gamma*(N-Ntr)*S-S/tp+beeta*gamma*N/tn';
=solve(Sin,'S');

Nin='I/(q*vact)-goi*(N-Ntr)*S/(1+epsilon*S)-N/tn';
Nin=subs(Nin,'S',S(1));
Nin=subs(Nin,'goi',goi);
Nin=subs(Nin,'Ne',Ne);
Nin=subs(Nin,'Ntr',Ntr);
Nin=subs(Nin);
Nin=vpa(Nin,10);

I=0:0.1e-3:60e-3;
T=[283 298 323 243];
for x=1:length(T),
S1=subs(Nin,'T',T(x));
for y=1:length(I),
S2=subs(S1,'I',I);
S2=vpa(S2,10);
[S3]=solve(S2,'N');
t(y,x)=0+1*i;
for z=1:length(S3),
if(isreal(S3(z)) && double(S3(z))>=0),
t(y,x)=z;
end
end
if(isreal(t(y,x))),
N(y,x)=double(S3(t(y,x)));
else
N(y,x)=0;
end
end
end



There is some problem in solvin this differential equation.... It is not able to solve for N even after subtitutin all varialbles....Please help me to rectify error or give some other suggestion to solve this code.....It doesnt give any error but to solve for single current value I and single temperature T , it runs out of my physical memory...which is set at 1900MB....