ContinuousNewtonMethod

The continuous Newton method involves solving a differential equation of the form:

\begin{equation} y'(t) = -\frac{f(y(t))}{f'(y(t))} \end{equation}

where $f$ is a differentiable function and $y(t)$ is a continuously varying approximation of the root of $f$. While closed-form solutions for the continuous Newton method are known for some special cases, such as when $f$ is a quadratic polynomial or the exponential function, for most functions $f$ no closed-form solutions are available. Therefore, numerical methods must be used to approximate the solution.