how to solve system of nonlinear equation

I have a set of nonlinear equation as

-(C1+C2)*x+C3*y-C4*x*y+1/4*C5*y^2+C6 = 0,....(1)

C2*x-(C3+C7)*y-5/4*C5*y^2+3*C6 = 0;.....(2)

I have all the constant values as, C1 = 3.2e7; C2 = 3.1e7; C3 = 5.6e3; C4 = 2e-11; C5 = 5e-15; C6 = 1.04e20; C7 = 8.2e2;

I have already used 'fsolve' with intilal guess [ 1e13 3e16], but it showed 'no solution found'. Please let me know if I have to change my guess or any other way to solve this. I have attached the code as well. Thanks.

Answer 1

[Stephan]

Hi,

vpasolve finds 3 solutions:

syms Ns0 Nt0
k_rs = 3.2e7;
k_ISC = 3.1e7;
k_RISC = 5.6e3;
k_ST = 2e-10; 
k_TT = 5e-15; 
k_NRT = 8.2e2;
d = 15e-7;
J = 0.1;
e = 1.6e-19*1e3;
eq1 = -(k_rs+k_ISC)*Ns0+k_RISC*Nt0-k_ST*Ns0*Nt0+0.25*k_TT*Nt0.^2+J/(4*d*e)==0;
eq2 = k_ISC*Ns0-(k_RISC+k_NRT)*Nt0-1.25*k_TT*Nt0.^2+(3*J)/(4*d*e)==0;
sol = vpasolve([eq1, eq2], [Ns0, Nt0]);
sol_Ns0 = sol.Ns0
sol_Nt0 = sol.Nt0

Best regards

Stephan

[Monirul Hasan]

Hi Stephan, Thanks a lot for your support. The solutions looks much realestic now. By the way as I know Ns0, Nt0>0, Can I put this conditions inside 'vpasolve' and is there a way to specify the search in specific range? Please let me know. Cheers.

[madhan ravi]

https://www.mathworks.com/help/symbolic/assume.html#buoccfj-1

https://www.mathworks.com/help/symbolic/vpasolve.html#bt5sqi5-1-init_guess

[Monirul Hasan]

Thanks a lot Stephan. It worked. I am accepting your answer. I am going work some more on that code. If you are ok, I might ask for some additional help on that as well.

[Stephan]

Feel free to ask more questions. Usually i unfollow questions, that have been solved so far. So it is a good idea to open a new question, if you have issues. Also new and unanswered questions are usually answered very quickly by Madhan Ravi ;-)

He has very good knowledge about Symbolic calculations in Matlab.