How can I solve this non-linear system?

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Yves Adou
Yves Adou 2021-4-3
编辑： Sam Chak 2024-5-30
EquationOne = @(x1,x2) 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EquationTwo = @(x1,x2) 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  2 个评论
darova
darova 2021-4-3
Do you have any attempts? What about numerical approach? What about contour?
Yves Adou
Yves Adou 2021-4-3
I tried the folling code for solving:
z = optimvar('z',2);
Eq1 = fcn2optimexpr(@(z)EquationsOne(z(1),z(2)),z) == 0;
Eq2 = fcn2optimexpr(@(z)EquationsTwo(z(1),z(2)),z) == 0;
prob = eqnproblem;
prob.Equations.Eq1 = Eq1;
prob.Equations.Eq2 = Eq2;
show(prob)
z0.z = [0 0];
[sol, fval, exitflag] = solve(prob,z0)
and I obained the following:

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回答（1 个）

Vidhi Agarwal
Vidhi Agarwal 2024-5-30
Hi Yves Adou,
I recognize that you're encountering an issue in solving 2 complex nonlinear equations. “fsolve” function from the Optimization Toolbox is commonly used for this purpose. Here’s the steps you can follow to solve the problem:
  1. Define the equation as anonymous functions in MATLAB.
  2. “fsolve" requires the equations to be in a single function if you have multiple equations. You can combine them into a single function that returns a vector.
  3. Before you call “fsolve”, you need to provide an initial guess for the values of “x1” and “x2”. If you don't have a good initial guess, you can start with zeros or any arbitrary values.
Here is the sample code demonstrating the same:
function solve
% Nested functions for the equations
function f1 = EquationOne(x)
f1 = x(1)^2 + x(2)^2 - 4;
end
function f2 = EquationTwo(x)
f2 = x(1) * x(2) - 1;
end
% Combined function for fsolve
function F = mySystem(x)
F(1) = EquationOne(x);
F(2) = EquationTwo(x);
end
% Initial guess: Adjusted based on the problem's feedback
x0 = [1.2, 0.8]; % Adjusted initial guess for potentially better convergence
% Options for fsolve: Adjust function tolerance and step tolerance
options = optimoptions('fsolve', ...
'FunctionTolerance', 1e-10, ...
'StepTolerance', 1e-10, ...
'Algorithm', 'trust-region', ...
'Display', 'iter'); % Showing iteration process for better insights.
% Solve the system with adjusted settings
[x, fval, exitflag, output] = fsolve(@mySystem, x0, options);
% Displaying the results
disp('Solution:');
disp(x);
disp('Function values at the solution:');
disp(fval);
end
Output of the following code will look like this:
For better understanding of “fsolve”, and optimization toolbox please refer to the following documentation:
Hope this helps!

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