MaplePrimes - answers and comments on Question, ODE w/power series....PLOTTING

odeplot

alec — Thu, 06 May 2010 08:26:14 Z

Perhaps, odeplot can be used. It's hard to guess without seeing the equations. The series solutions are not good for plotting in this example. You could get a plot by removing the O term (the last one) in the series, but it may be very far from the actual plot.

Alec

PS ?odeplot doesn't provide a link to the help page. Is it broken now? -Alec

Removing the order term from a series

Robert Lopez — Thu, 06 May 2010 23:01:25 Z

RJL Maplesoft

In particular, to remove the "big oh" term from a series S, use

convert(S,polynom);

This effects a change in the internal structure of the object. The internal representation of a series does not allow for evaluation or plotting. Simply removing the O-term wouldn't help either. It's the internal representation that has to change, and the convert command does that, as well as remove from the display the O-term.

It's possible to make this conversion interactively through the Context Menu. Select Series->Truncate to polynomial.

This option activates the convert command, although on the screen it will appear that all that has happend is that the expression has been truncated.

thank you

arrighi — Thu, 06 May 2010 23:15:51 Z

I will try this and get back to you

odeplot

Robert Israel — Fri, 07 May 2010 01:16:58 Z

?odeplot works fine for me in Maple 13.02 and Maple 14. In Maple 12 Classic you need ?plots,odeplot.

But odeplot is for an output of dsolve(..., numeric), not dsolve(..., series).

numeric

alec — Fri, 07 May 2010 01:54:50 Z

There is a possibility that the problem was to use dsolve(..., series) to construct the plot, but it seems more probable that the problem was to find an approximate solution and to draw a plot.

In the posted partial sum, the absolute values of the last 3 coefficients are greater than 1/(1.5)^13, 1/(1.5)^14, and 1/(1.5)^15, correspondingly, so it can not be used for plotting on distances 1.5 from 1 or greater - in particular, for x=4.

I meant ?odeplot or ?plots,odeplot on this site - it used to work like that, producing (automatically) a link to the corresponding help page.

Alec

removing the order

alec — Fri, 07 May 2010 18:16:29 Z

Well, I pasted the example from the original post in Maple and removed the order term without any problems just by deleting it. That doesnt solve the plotting problem though because the series seem to have the radius of convergence close to 1.5, and centered at x=1 - so the partial sum could be used reliably for plotting only on the beginning of the interval from x=1 to x=4 - say for x from 1 to 2, and has very little to do with the plot of the actual solution at the end of the interval - for x from 3 to 4.

Alec