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From: Chris Carlen
User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.0.0) Gecko/20020529
X-Accept-Language: en-us, en
Subject: Fun with calculators
Date: Sun, 08 Sep 2002 17:21:36 GMT
NNTP-Posting-Date: Sun, 08 Sep 2002 10:21:36 PDT
I recently posted to comp.sys.hp48 a question to see if an HP calculator
could solve the following differential equation numerically:
and with the function id(vd)=1E-14*(e^(38.9411*vd)-1). Yes, that is a
diode current vs. voltage function.
y[t] in this problem represents the output voltage of a half wave
rectifier driven by an ideal 10V 50Hz sinewave voltage source into a
100uF filter cap and 100 ohm load resistor.
A TI-89 calculator can solve this using Runge-Kutte in just over 6
minutes, 200 points from t=0 to t=0.1 seconds.
Mathematica 4.1 takes 0.01 seconds using Gear integration on an Athlon
XP1600 with .5GB RAM and running Linux, of course. But I had to fuss
with the accuracy parameters a lot to get it to go. RK on MMA fails to
solve it at all.
SPICE is a cool program, since it seems to be so highly optimized to
handle these sharp cornered solutions. Maybe some math geniuses can
comment on the mathematical theory of stiff diff. equations.
Someday I'd like to have a hand calculator or PDA that can do stuff like
this quickly. Maybe a Sharp Zaurus, in a few more years when they get a
little cheaper. Probably can run Octave (Matlab clone), the original
Linux SPICE, and the symbolic package Maxima on that. A Linux number
crunching workstation in the palm of my hand! There's also some
interesting handheld PCs out there.
Anyone have some other interesting underpowered computers they want to
try to solve this with?
Christopher R. Carlen
Suse 7.3 Linux 2.4.10
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