
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

