solving nonlinear system of equations
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I have a set of non-linear equations that I want to solve. I tried to specify a value for x3 from which I hope Solve function will help me find corresponding solution/solutions. For some reason, the solution solved by matlab contains a different value for x3. Here are the equations
i=0.1;
syms x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 O positive
[x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 O] = solve(...
x3==i,...
x1==(k11*O+k12*(N-O))*(k1*x5)/(1+k1*x5)/(muD+lamQs),...
x3==(k11*O+k12*(N-O))/(1+k1*x5)/(muD+lamQl),...
x5*(lamQar*muD)==k21*O+k22*(N-O)-(k11*O+k12*(N-O))*(k1*x5)/(1+k1*x5),...
x2==1,x4==1,...
x7*(k31+lameI)==k3*(x1+x3)*Vcon+k31*x6,...
x6==k31*x7/(k31+lamiI+muD),...
x8==k32*x9/(k32+lamiC+muD),...
O==N*x10/(x10+Kb*x11),...
x10==k41*x12^4*x6^4/(lam+muD),...
x11==k42*x12^4*x8^4/(lam+muD),...
x12*(lamPrg+muD)==(k51*O+k52*(N-O)),...
x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,O);
Here are the set of parameters if you need to try:
N=5/0.602;
k11=7.23*10^-3; %kQl
k12=8.871*10^-2; %kQul
k21=1.021*10^-2; %kQal
k22=1.21*10^-3; %kQaul
k1=10^-2; %kQb
k3=10^-2; %ki
Vcon=1;
k31=10^-4; %kTi
k32=10^-3; %kTc
Kb=10^-6;
lamQs=10^-4;
lamQl=0.1;
lamXar=3.851*10^-4;
lamQar=10^-3;
lamX=10^-4;
lameI=10^-6;
lameC=10^-6;
lamiI=10^-6;
lamiC=10^-6;
lam=10^-6;
lamPrg=10^-6;
k51=10^-6;
k52=10^-5;
k41=10^-12;
k42=10*k41;
muD=log(2)/(45*60);
The solutions that i got containing x3=62.8957 Thanks, Vu
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