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Topic: Numerical ODEs
Replies: 10   Last Post: May 16, 2013 4:22 PM

 Messages: [ Previous | Next ]
 Roland Franzius Posts: 586 Registered: 12/7/04
Re: Numerical ODEs
Posted: May 12, 2013 12:44 PM

Am 12.05.2013 17:02, schrieb José Carlos Santos:

> 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?

f=g^2

Then you have

2 g g' = 2 Abs(g)

This equation has three solutions

g=0

or g!=0

g'=sign(g), g=+-x

which make two solutions for f.

--

Roland Franzius

Date Subject Author
5/12/13 Jose Carlos Santos
5/12/13 Roland Franzius
5/12/13 Peter Percival
5/13/13 Jose Carlos Santos
5/13/13 Roland Franzius
5/13/13 David C. Ullrich
5/13/13 Jose Carlos Santos
5/14/13 Niels Diepeveen
5/15/13 Bart Goddard
5/16/13 Jose Carlos Santos
5/16/13 Bart Goddard