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

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Jose Carlos Santos

Posts: 4,896
Registered: 12/4/04
Re: Numerical ODEs
Posted: May 16, 2013 1:20 PM
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On 15-05-2013 21:15, Bart Goddard wrote:

> Pretty much out of my field, (I'll do anything to avoid grading
> final exams) but I notice that if you take the
> derivative of both side of the DE and substitute, you discover
> that f''(x)=2. As I understand, Runge-Kutta approximates the
> second derivative and self-adjusts itself to account.

This works indeed for the ODE f'(x) = 2 sqrt(f(x)), but, more
generally, I am interested in ODEs of the type f'(x) = g(f(x)), under
the initial condition f(0) = 0 and where g(0) = 0. Then, all I get is:

f''(x) = g'(f(x))*g(f(x))

and I don't see how to proceed from here.

Best regards,

Jose Carlos Santos

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