Re: Back Euler with error control

Fred Krogh wrote:
>
> > Pick an h, integrate, then repeat with h/2, compare the results (at h)
> > against tolerances (rel & abs), proceed if met, else cut h in half again
> > until tolerance are met, and so on.
>
> Although it can be tricky to get the error control right, almost
> anything is likely to be better than this...
> This advice would have you using this small stepsize for
> the entire integration or getting significant errors early on, which in
> some cases would have you getting onto an incorrect solution. I suspect
> your teacher or your text book has something fairly easy to implement
> that will serve together with the above advice, except that instead of
> halving h, one tries for different error tolerances.

It seems you missed the gist and then got lost in speculatives. It
wouldn't have been much of an adaptive scheme if the minimum step (on
interval h) would have been used from there to eternity. With that
factored in, they don't get any better, or simpler, however we'd be all
ears if you list some of that *almost anything better* you alluded to.

.

Relevant Pages

  • Re: Back Euler with error control
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    (sci.math.num-analysis)
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