Re: Some FEM questions

From: Peter Spellucci (spellucci_at_fb04373.mathematik.tu-darmstadt.de)
Date: 01/13/05 

Date: Thu, 13 Jan 2005 15:33:43 +0000 (UTC)

In article <n8ekvpf3xgtd@legacy>,
 faircdl@auburn.edu (Daniel Faircloth) writes:
>On Tue, 11 Jan 2005 17:19:37 +0000 (UTC), Peter Spellucci wrote:
>> "in principle" yes
>> you get a stiff equation and integrating this one by an explicit
>method
>> requires a time step of magnitude
>> delta_time <= constant * delta_space_squared (!)
>> better than using this Euler explicit for the ODE use the
>specialized
>> Runge-Kutta-scheme of Verwer-Sommeijer "rkc.f" available from
>> http://www.netlib.org/ode
>
>Can Runge-Kutta methods be used even when you system of ODE's is of
>the form [M]du/dt+[K]u-f=0 where [M] and [K] and matrices?
>

yes, you add a linear system solver in evaluating the "k_i"-s (the
increments), that means you first simulate as if you had made the
ode explicit by multiplying with inverse(M), write down the equations for
the runge-kutta-step, then multiply back with M and you get the equations
e,g, matlab ode45 does this if you provide a massmatrix via "odeset".
hth
peter