I have a differential equation taken from eq(5.12) of this paper.

$$-4rdot{r}^2 + 2 r^2 ddot{r}+frac{4}{r^2}dot{r}^3sin^3(xi)cos(xi)+dot{r}^3 r^2 sin(xi)=0$$

Where $xi$ is a variable of the function $r=r(xi)$ with conditions $lim_{xirightarrow 0}r(xi)=infty$, $r(pi)=0$. In the paper, the authors claim that one can solve this with gradient flow.

I tried to look up a numerical method that uses gradient flow but can not find a good reference for this method (I am completely a noob in a numerical method so this might be a well-known method?). If anyone is familiar with such a numerical method, It would be very helpful if you could direct me to a reference for this.

Thank you