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NDSolve problem with piecewise functions
*To*: mathgroup at smc.vnet.net
*Subject*: [mg32065] NDSolve problem with piecewise functions
*From*: "Christopher R. Carlen" <crcarle at sandia.gov>
*Date*: Fri, 21 Dec 2001 03:57:45 -0500 (EST)
*Organization*: Sandia National Laboratories, Albuquerque, NM USA
*Sender*: owner-wri-mathgroup at wolfram.com
Hi:
I am using NDSolve in Mathematica 4.1.0.0 to do time-domain transient
electrical circuit analysis. I have a very simple RC high-pass filter
circuit. I want to calculate the output waveform when it is excited by
various waveforms.
However, I am having problems with the output of NDSolve not making
sense with certain excitation functions.
For example:
f[t_] := 1.0 Sin[2 Pi 60.0 t]
Plot[f[t], {t, 0, 2/60}] (* looks like a sinewave with amplitude 1.0 *)
HighPass =
NDSolve[ { D[Vhp[t] - f[t], t] + 1.0 Vhp[t] == 0, Vhp[0] == 0.},
Vhp, {t, 0, 2/60}, MaxSteps -> 10000 ]
(* that's a 60 Hz sinewave into a 1Hz cutoff filter, should come through
with almost no amplitude attenuation *)
Plot[ Vhp[t] /. HighPass[[1]], {t, 0, 2/60} ]
(* looks great, still has amplitude of about 1.0 *)
Clear[f]
(* Now define a piecewise function that represents a sinewave with
amplitude clipping *)
BigSine[t_] := 2.0 Sin[2 Pi 60.0 t]
f[t_] := 1.0 /; BigSine[t] > 1.0
f[t_] := BigSine[t] /; (BigSine[t] < 1.0 && BigSine[t] > -1.0)
f[t_] := -1.0 /; BigSine[t] < -1.0
(* go back and plot, resolve the equation, and plot the output. There
is no reason for the amplitude to be now 0.5 instead of 1.0 . The shape
makes sense, but the amplitude is 1/2 of what is expected. What's going
on? *)
Something seems to go wrong when using the piecewise excitation function
in NDSolve. I need to understand how to get this to work reliably,
because I need to do this a lot, with eventually more complicated
equation sets. I have done other NDSolves with piecewise defined
functions in the past without running into this problem.
Strange.
Help appreciated greatly!
____________________________________
Christopher R. Carlen
Principal Laser/Optical Technologist
Sandia National Laboratories CA USA
crcarle at sandia.gov
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