MATLAB: Explict (pointwise) function from numerical solution to implicit equation

implicit equationnumerical solution

I can plot the numerical solutions to a complicated expression f(x,y)=0 over intervals for x and y using fimplicit(f,interval). However, how do I then define/specify an explicit relation y=g(x) pointwise using the numerical values computed from f(x,y)=0 for use in a separate expression? (There is a functional relation.)

Best Answer

Try interp1 to create an explicit relation for 'y' in term of 'x' using the datapoints from fimplicit
f = @(x, y) y - x.^2;
fp = fimplicit(f, [-2 2 0 10]);
x = fp.XData;
y = fp.YData;
g = @(xq) interp1(x, y, xq);
Then run
>> g(1)
ans =
    1.0002
>> g(0.5)
ans =
    0.2501
Alternate solution:
Use fsolve() directly. The advantage is that you can control the spacing of x-points
f = @(x, y) y - x.^2;
x = -2:0.01:2;
y = fsolve(@(y) f(x, y), rand(size(x)));
g = @(xq) interp1(x, y, xq);
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