I am trying to find nonstandard finite difference scheme for a nonlinear ordinary differential equation with square term in denominator. I am working on a ecological model with complicated nonlinear term on the right hand side. But here I am presenting a simple example, if I can find the scheme for the following problem that will be helpful for my model:
$\frac{dx}{dt}=\frac{x^2}{1+x^2}$
I searched google and find many resources but no one explained about such ODE. I found one research paper by R. E. Mickens where he mentioned that he is working on it but did not find any update (I think paper was published ten years ago).
Any clue will be helpful in this regard. Thanks.