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