Re: dsolve/numeric

From: Annie (ayuk_at_cs.toronto.edu)
Date: 01/17/05 

Date: Mon, 17 Jan 2005 21:35:32 +0000 (UTC)

On Mon, 17 Jan 2005 15:07:00 -0500, Carl Devore wrote:
>On Mon, 17 Jan 2005, Annie wrote:
>> I would like to use the result of a dsolve/numeric command as input
to
>> the Pade command. For example, I would like to use the result of
>> something like:
>>
>> dsolve(ode union IC, {u1(t), u2(t), type=numeric,
output=listprocedure);
>>
>> and then obtain the Pade of u1 and u2, something like:
>> unapply(pade(u1(t),t,[9,10]),t).
>
>If you can only give numeric input, then you'll have to settle for a
>Chebyshev-Pade approximation on an interval. For example:
>
>> S:= dsolve(
>> {diff(y(x),x)=y(x), y(0)=1}, {y(x)}
>> ,type=numeric, output=listprocedure
>> );
>
> S:= [x=(proc(x)...end proc), y(x)=(proc(x)...end proc)]
>
>> f:= rhs(S[2]):
>> with(orthopoly):
>> Pade:= numapprox[chebpade](f, -1..1, [2,2]);
>
> 2
> 0.9617620445 + 0.4849343797 x + 0.08048275453 x
> Pade := x -> ------------------------------------------------
> 2
> 0.9617228410 - 0.4764292903 x + 0.07655431802 x

Thanks for the suggestion. Greatly appreciated.