Re: [ng-spice-devel] FYI: backward Euler, trapezoidal, Gear
> Runge-Kutta is a very poor choice, and has no place in circuit
> simulation. The mapping places a large part of the S stable region
> outside of the Z unit circle, mapping the stiff poles into the
> unstable region. Besides that, it is harder to implement in this
> context.
I aggree with most of the things you talked about. But i think that
your position on Runge-Kutta methods in not really the good one. Most
of the people when talking about RK methods think about the classical
RK methods using explicit schems. But nowadays research activities
are made about IRK (implicit runge-Kutta methods). These methods are
adapted as BDF methods to stiff problems. We can sinthetise A-stable
IRK methods of higher order.
As One-step methods and self-starting there are well suited to
problems with many discontinuities as in switching circuits. The
major drawbacks are the poor step control schemes and the fact that
the function are evaluated many times by timestep. For the step
control research activities are going on.
So i think that something can be made with RK in the future. For now
they can be used to start BDF methods with an high order instead of
starting by BE and increasing order at each step. They can be used
also in switching circuit simulation (power electronics for instance
or switching capacitor circuits) to bypass the necessary restarting
process of BDF methods when a discontinuity is found.
I wrote a paper this year for IASTED (Innsbruck Feb 2000) where it is
shown that IRK can be used for switching circuits because it exists
one class of IRK methods which gives the correct solution even if the
initial conditions of a DAE are not consistent.
Do you know that One of the first order IRK methods is Backward Euler
and the trapezoidal rule is also an Implicit Runge Kutta method?
Sincerely.
Dezai GLAO.
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