Solve a system of 4 non linear equations with symbolic expressions

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Nordine Bouchelia
Nordine Bouchelia 2022-5-27
评论： Walter Roberson 2022-5-27
Hello,
Could you tell me please the way to solve this system of equations using Matlab ?
Thanks for your help,
h = ((zeta*(1-u))/(gamma*(1+eta-n*eta)-1))^(1/(alpha*theta))*((theta*(1-alpha)*(1-tau_l)*A)/(1-theta))^(1/alpha)*u^(-1);
c = (((1-beta)*n*eta*gamma)*(b+1-delta+alpha*A*(h*u)^(1-alpha)*(1-tau_k)))/(beta*(1-delta+alpha*A*(h*u)^(1-alpha)*(1-tau_k))-1+n+n*eta);
b = (A*(h*u)^(1-alpha)*(d-tau_l*(1-alpha)-alpha*tau_k)*(1-delta+alpha*A*(h*u)^(1-alpha)*(1-tau_k)))/((1+n)*gamma-1+delta-alpha*A*(h*u)^(1-alpha)*(1-tau_k));
gamma = (A*(h*u)^(1-alpha)*(1-d-((theta*(1-alpha)*(1-u)*(1-tau_l))/((1-theta)*u)))-c+1-delta)/(1+n);
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Nordine Bouchelia
Nordine Bouchelia 2022-5-27
I think we'll opt for numerical simulation. Last question, I think Matlab simulink can help with numerical simulation as well as Octave right ?
Thanks for your time and explanations, in fact you were very clear.
Walter Roberson
Walter Roberson 2022-5-27
At the moment I cannot think of any way that Simulink would be useful for this purpose.
I have no information about the quality of Octave implementation of relevant routines.

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回答（1 个）

Sam Chak
Sam Chak 2022-5-27
编辑：Sam Chak 2022-5-27
Hi @Nordine Bouchelia
You can follow the examples in
https://www.mathworks.com/help/optim/ug/fsolve.html
to create a function m-file and write the equations in the form .
function F = root2d(x)
F(1) = exp(-exp(-(x(1) + x(2)))) - x(2)*(1 + x(1)^2);
F(2) = x(1)*cos(x(2)) + x(2)*sin(x(1)) - 0.5;
end
Then, in the command window, type:
fun = @root2d;
x0 = [0, 0]; % guess initial point of the solution [0, 0].
x = fsolve(fun, x0)
x =
0.3532 0.6061
If you prefer solving the problem symbolically, you can use the solve function and refer to this link:
https://www.mathworks.com/help/symbolic/solve.html

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