```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, buthere it goes.In what follows, I am only interested in functions defined in someinterval 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 asolution of this ODE. The problem is that I am not interested in thatsolution; the solution that I am after is f(x) = x^2.For my purposes, numerical solutions are enough, but if I try to solvenumerically an ODE of the type f'(x) = g(f(x)) (with g(0) = 0) andf(0) = 0, what I get is the null function. So far, my way of dealingwith this has been to solve numerically the ODE f'(x) = g(f(x)) andf(0) = k, where _k_ is positive but very small and to hope that thesolution that I get is very close to the solution of the ODE that I aminterested in (that is, the one with k = 0). Do you know a better wayof dealing with this problem?Best regards,Jose Carlos Santos
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