Re: LaPlace Transforms in TI89 and HP48 compared by Perez-Franco
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Re: LaPlace Transforms in TI89 and HP48 compared by Perez-Franco
You missed another conclusion: the TI-89 is faster than the HP-48.
--
Daniel Moraseski
http://members.xoom.com/spui/ - FL and NJ roads
King of irrelevant info
in Orlando, FL (A SPUI has been found at TOLL 4080 (the connector from 408
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originally from Manalapan, NJ (near US 9 and NJ 33) (there will probably
never be a SPUI there)
Perez-Franco wrote in message <77tjoa$53e$1@nnrp1.dejanews.com>...
>[ LaPlace Transforms in TI89 and HP48 compared by Perez-Franco ]
>
>I've developed a way to solve LaPlace transforms in my new TI-89 (presented
>below) and I wanted to compare its speed and performance with other
proposals
>for LaPlace I've seen.
>
>In HP48GX, we solved LaPlace transforms using the great program by Bernard
>Parisse: Erable (ver 3.1). We used z LAP EXPA.
>
>In TI-89 we used three ways:
>
>1) First LaPlace proposal by Pirez-Franco
>-'(e^(-s*t)*z,t)|t=0
>using 20 bytes.
>
>2) Second LaPlace proposal by Pirez-Franco
>-limit('(e^(-s*t)*z,t),t,0)
>using 27 bytes.
>
>3) LaPlace proposal by elrond
>'(z*e^(-s*t),t,0,infin)|s>0
>using 23 bytes.
>
>Answers were verified in MapleV for accuracy, using the following line:
>> with(inttrans): simplify(laplace(z,t,s));
>
>In all these lines, z is the function which we want to transform and ' is
the
>integration symbol.
>
>Let's check out the time it took to solve the LaPlace transforms of some
>function using the different tools.
>
>Function 1): 1
>HP48GX+Erable: Less than 1
>LaPlace P-F#1: Less than 1
>LaPlace P-F#2: Less than 1
>LaPlace elrond: Less than 1
>
>Function 2): 3*sin(5*t)
>HP48GX+Erable: 5 sec
>LaPlace P-F#1: Aprox 1 sec
>LaPlace P-F#2: Aprox 1 sec
>LaPlace elrond: Aprox 1 sec
>
>Function 3): 1+t+t^2+t^3
>HP48GX+Erable: 5 sec
>LaPlace P-F#1: Aprox 3 sec
>LaPlace P-F#2: Aprox 3 sec
>LaPlace elrond: 45 sec
>
>Function 4): 2*sin(2*t)+3*sin(3*t)+4*sin(4*t)
>HP48GX+Erable: 16 sec
>LaPlace P-F#1: Aprox 3 sec
>LaPlace P-F#2: Aprox 3 sec
>LaPlace elrond: Aprox 3 sec
>
>Function 5): 4+3*t^2+cos(5*t/3)
>HP48GX+Erable: 9 sec
>LaPlace P-F#1: Aprox 2 sec
>LaPlace P-F#2: Aprox 2 sec
>LaPlace elrond: Didn't finished in 6 minutes...
>
>Function 6): 4*t*cos(3*t)
>HP48GX+Erable: 6.5 sec
>LaPlace P-F#1: 6 sec
>LaPlace P-F#2: 7 sec
>LaPlace elrond: 48 sec
>
>Function 7): 4*t*cos(3*t+Pi/3)
>HP48GX+Erable: Gived wrong answer, -2/s^2.
>LaPlace P-F#1: 20 sec
>LaPlace P-F#2: 22 sec
>LaPlace elrond: 80 sec
>
>As we can see, in speed and performance, the best proposal by now is to
solve
>LaPlace transforms using -'(e^(-s*t)*z,t)|t=0 . I suggest using it as a
user
>defined function called lap() which can be done by typing in your TI-89
this
>line:
>
>Define lap(z)=-'(e^(-s*t)*z,t)|t=0
>
>Comments are welcome to hplus@i.am
>
>- Roberto Perez-Franco
>
>-----------== Posted via Deja News, The Discussion Network ==----------
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