Date: May 12, 2013 11:02 AM
Author: Jose Carlos Santos
Subject: Numerical ODEs
Hi all,

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 an ODE of the type f'(x) = g(f(x)) (with g(0) = 0) and

f(0) = 0, what I get is the null function. So far, my way of dealing

with this has been to solve numerically the ODE f'(x) = g(f(x)) and

f(0) = k, where _k_ is positive but very small and to hope that the

solution that I get is very close to the solution of the ODE that I am

interested in (that is, the one with k = 0). Do you know a better way

of dealing with this problem?

Best regards,

Jose Carlos Santos