```Date: May 13, 2013 11:30 AM
Author: Jose Carlos Santos
Subject: Re: Numerical ODEs

On 13/05/2013 14:53, dullrich@sprynet.com wrote:>> 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?>> I suspect you may never get the sort of answer you want here.> There are those numerical methods out there. The proof that> they work typically depends on certain hypotheses, which> hypotheses typical entail the existence and uniqueness of> the solution. You have a DE that does not satisfy those> hypotheses, so you shouldn't expect those methods to> give the solution you want.You are probably right. :(Best regards,Jose Carlos Santos
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