So it seems I've uncovered a Maxima bug - and been given a workaround.
My question stemmed from trying to use Maxima to obtain errors for
numerical integration methods. For example, for the Newton-Cotes rule of
order 2 (Simpson's rule), we have
integrate(f(x),x,a,a+2*h) = (h/3)*(f(a)+4*f(a+h)+f(a+2*h)) + Error
and an expression for the error (as a series) can be obtained by expanding
(f(x) and its integral as Taylor series and cancelling terms. Maybe
there's a way of doing this without using Maxima's "taylor" function?
Thanks,
Alasdair
On Mon, May 13, 2013 at 5:21 AM, Dennis J. Darland <
student at dennisdarland.com> wrote:
> **
>
> I really mean a general method for funcions within a neighborhood where
> they are analytic.
>
>
>
> --
>
> Dennis J. Darland
>
> student at dennisdarland.com
>
> http://dennisdarland.com/
>
> http://dennisdarland.com/philosophy/
>
> http://sode.sourceforge.net/
>
>
>
> On Sunday, May 12, 2013 01:55:12 PM Dennis J. Darland wrote:
>
> "The Method of Frobenius"
>
>
>
> It seems limited to one second order equation.
>
> (which some other methods fail for)
>
>
>
> See
>
> http://en.wikipedia.org/wiki/Frobenius_method
>
>
>
> I was asking about a general way.
>
> --
>
> Dennis J. Darland
>
> student at dennisdarland.com
>
> http://dennisdarland.com/
>
> http://dennisdarland.com/philosophy/
>
> http://sode.sourceforge.net/
>
>
>
> On Sunday, May 12, 2013 11:16:40 AM you wrote:
>
> On 5/12/2013 10:22 AM, Dennis J. Darland wrote:
>
> I have a question.
>
> Is there a way to get the Taylor series (symbolically) of functioons
> which represent the solutions of systems (possibly nonlinear and higher
> order) of ordinary differential equations?
>
> Yes, e.g. Method of Frobenius, for example.
>
> That is what my omnisode program does - except just numerically.
>
> --
>
>
>
>
>
>
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>
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