>> This question is perhaps too vague to have a meaningful answer, but >> here it goes. >> >> In what follows, I am only interested in functions defined in some >> interval of the type [0,a], with a > 0. >> >> Suppose that I want to solve numerically the ODE f'(x) = 2*sqrt(f(x)), >> under the condition f(0) = 0. Of course, the null function is a >> solution of this ODE. The problem is that I am not interested in that >> solution; the solution that I am after is f(x) = x^2. >> >> For my purposes, numerical solutions are enough, but if I try to solve >> numerically > > What method are you using? I'm just being curious, I don't know a > solution to your problem.
I use Mathematica and, more specifically, the NDSolve command. I suppose that the default method that it uses is the Euler method.