Numerically solving piecewise system of equations

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Jeremy Mercer
Jeremy Mercer 2021-8-23
I am using vpasolve to numerically solve systems of equations. I tried to solve a problem that had a piecewise function in it and it did not work. I made the simplest problem I could that replicated the issue below to troubleshoot the issue. If I set the initial parameters to the exact answer ([0.5,0.25]), MATLAB confirms the solution. If I set the initial parameters slightly away from the solution (for example [0.5,0.24999]), the function fails to find a solution.
function [Out] = piecewise_test
a=-0.25;
% a=1;
syms x y
eqn1 = y == x+a;
% if abs(x)>=1
% eqn2 = y == abs(x);
% else
% eqn2 = y == x^2;
% end
eqn2 = y == piecewise(abs(x)>=1,abs(x),x^2);
sol=vpasolve([eqn1, eqn2],[x, y],[0.5,0.25])
Out=[sol.x, sol.y];
end
In the full problem, the solution can be predicted decently within a range, so using initial parameters is fine as long as it can find the answer within 1 order of magnitude of the initial parameter.
I am looking to calculate a numerical solution and I am ignoring any complex or negative solutions. I want to keep solve time down if possible as the function runs at least 200 times in my code.

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