I'm researching a topic for solving general algebraic equations using numerical method. My numerical recipe knowledge is rather rusty with the Bisection to Newton's methods but I don't think those could be applied for equations such as:
$$ \frac{x^2}{2+x}+\cos(x+1)=x^2\times \sin\left(\frac{\sqrt x}{x^2}\right) $$
with an approximated numerical solutions: $$ x_1\approx0.531709 $$ and $$ x_2\approx3.401750 $$ I know matlab has the vpasolve function for numerical approximation of the unknown variable but I can't find any details regarding the used method or even if such a numerical method exist that can be used to approximate the unknown variable for any given equation with one unknown var. At first I tried applying Newton Raphson's method but stuck right at the beginning since:
- I'm not searching for a solution in the form of $f(x)=0$.
- I don't know the derivative for the equation and I don't want to apply symbolic algorithms.
Thank you for the tips! Cheers!