Re: NDSolve problem with switching

• To: mathgroup at smc.vnet.net
• Subject: [mg106251] Re: NDSolve problem with switching
• From: Albert Retey <awnl at gmx-topmail.de>
• Date: Wed, 6 Jan 2010 06:00:03 -0500 (EST)
• References: <201001030842.DAA10093@smc.vnet.net> <hhun8c\$ngg\$1@smc.vnet.net>

```Hi,

> Here are simpler choices for the box wave.
>
> box[x_] = Piecewise@{{1, FractionalPart@x < .5}}
> Plot[box@t, {t, 0, 2}]
>
> or
>
> box = If[FractionalPart@# < .5, 1, 0] &;
>
> But, strangely enough, they don't speed things up in NDSolve.
>

I think there is no reason to expect they would. I think the problem is
that a numeric differential equation solver will always use a lot of
sampling points near one of the steps. Actually the resolution it will
use is just limited by the precision it tries to achieve, since it would
need infinitesimaly small steps to resolve the step. So if you want to
see speedup, one pragmatic approach would be to use a "smoothing" of
your step function, e.g. by replacing it with an appropriate ActTan.
Then you can control the resolution of the step function independently
of the desired precision. In most pratical problems you will have an
idea about what a reasonable resolution for such a step function would be...

hth,

albert

```

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