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From: Ross Anderson on 26 Jul 2010 20:36
Hi all,

I'm using ode15i to solve a system of DAEs. One of the terms is a time average of a function over the interval of integration dT. If I supply a tspan = [t0, t1, t2, ..., tf] to ode15i as well as my function, I can recover the dT being used:

[T Y] = ode15i(@(t,y,yp) yprimefunc(t,y,yp,tspan),tspan,0,0);
function Z = yprimefunc(t,y,yp,tspan)
tstep = find(t==tspan);
dT = tspan(tstep)-tspan(tstep-1);
Z = y-yp;
end

But picking a standard tspan=linspace(t0,tf,N) to supply to ode15i makes the convergence very slow. Allowing it to choose its own tspan=[t0, tf] speeds this up, but I still need to know the dT the solver is using. How can I recover that in my DAE function?
From: Torsten Hennig on 26 Jul 2010 23:08
> Hi all,
>
> I'm using ode15i to solve a system of DAEs. One of
> the terms is a time average of a function over the
> interval of integration dT. If I supply a tspan =
> [t0, t1, t2, ..., tf] to ode15i as well as my
> function, I can recover the dT being used:
>
> [T Y] = ode15i(@(t,y,yp)
> yprimefunc(t,y,yp,tspan),tspan,0,0);
> function Z = yprimefunc(t,y,yp,tspan)
> tstep = find(t==tspan);
> dT = tspan(tstep)-tspan(tstep-1);
> Z = y-yp;
> end
>
> But picking a standard tspan=linspace(t0,tf,N) to
> supply to ode15i makes the convergence very slow.
> Allowing it to choose its own tspan=[t0, tf] speeds
> this up, but I still need to know the dT the solver
> is using. How can I recover that in my DAE function?

lim (deltat->0) int_{t0}^{t0+deltat} y(t) dt / deltat
= y(t0)

So for deltat small, the average of a function f over
the interval [t0;t0+deltat] is just f(t0).

Or :

If you need the average u of a function f over the
interval [tstart,t], you can solve the differential
equation
du/dt = (f(t)-u(t))/(t-tstart)
with u(tstart) = f(tstart)
in u.

Best wishes
Torsten.
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