[TI-M] Ball-buster differential equations

To: ti-math@lists.ticalc.org
Subject: [TI-M] Ball-buster differential equations
From: Chris Carlen <crobc@earthlink.net>
Date: Fri, 06 Sep 2002 11:22:41 -0700
Reply-To: ti-math@lists.ticalc.org
User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.0.0) Gecko/20020529


Hi:

I am interseted in plotting and analyzing the data from differential 
equations typical of electrical circuit analysis with non-linear 
elements on the TI-89.

My present equation derives from the simplest case of a half-wave 
rectifier driving a filter capacitor in parallel with a load resistor.

The equation is:

t0=0
y1'=-y1/(100*100E-6)+id(-y1+10sin(2 pi 50 t))/100e-6
yi1=0

or with the numerics simplified for easier typing:

y1'=-100y1+id(-y1+10sin(2 pi 50 t))/1e-4

where the function id is defined as:

:id(vd)
:1E-14*(e^(1.609E-19*vd/(1.381E-23*298))-1)

I am using Rk to solve it, with the following parameters:

FLDOFF

t0=0
tmax=.1
tstep=.001
tplot=0
xmin=0
xmax=.1
xscl=0
ymin=-12
ymax=12
yscl=0
ncurves=0
diftol=.001 to .05 and various other tries.


The thing plots the right solution with these settings, but it is 
painfully slow.  Euler fails, giving nonsense results.  I expect that a 
problem of this sort, while being only a case of the simplest non-linear 
electric circuit problem, is really at the very limit of the machines 
abilities.

Is there any likelyhood of plotting this problem faster?

Ultimately I could be attempting systems of up to two or three coupled 
second order equations, reduced of course to the larger system of first 
order equations.  But it seems unlikely that the machine can pull 
something like this off.

Comments appreciated.
-- 
_____________________
Christopher R. Carlen
crobc@earthlink.net
Suse 7.3 Linux 2.4.10