[ODE] Runge-Kutta, Euler

Nguyen Binh ngbinh at gmail.com
Sat Mar 11 15:31:13 MST 2006


On 3/11/06, Josef <joseffojdl at gmail.com> wrote:
> Hi all,
> i'am writing my master thesis about solving ordinary differential
> equatations and i think physical engines would be a good example to compare
> the speed and the accurateness of the methods. But i have some questions and
> didn't find anything on the internet. I thought maybe someone here can help
> me.
> - Which methods are generally used in modern phsyic engines (Runge Kutta
> etc.)?

Mostly, implicit  Euler. Some use explicit Euler.

- Is the integration generally a bigger or a smaller problem compared to
> others ?

It's hard to answer this  question  fully.
I'll show you the case for RK45 and hope you can understand  the situation,
There can be 2 major ways to implement RK45:
+ Just blindly us RK45 with current engine: you can do that, but you won't
gain anymore accuracy(maybe just a little but surely not significant) . The
reason is right now almost all physics engine only go down to
velocity,i.ejust 2nd order in Taylor series so there is no gain for
using RK45. Note
that, this approach maybe rooted from Stewart-Trinkle time stepper.
+ Re write ST time stepper to use RK45. I don't really know if this apporach
is feasible. Because the time stepper that use trapezoidal method,one order
higher than Euler, results in a Nonlinear Complementarity problem and it's
much harder to solve than Euler. That's why I can say explicit Euler should
be the best for physics engine this time.

Binh Nguyen
Computer Science Department
Rensselaer Polytechnic Institute
Troy, NY, 12180
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