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
So what? I'm sure the TI89 is faster than the HP48 at almost everything!
However, the HP48 is at least 8 years old and the TI89 is less than one. I
think that's pathetic, someone who buys a TI has to wait 8 years to buy
something that beats the HP. That's not completely true either, considering
many people, including me, still like the HP48 over the TI89 (I've used the
TI92
for a few weeks) and the HP can still do many things that the TI can't.
Anyways, the HP calculator is a solid investment, and when/if HP comes out with
a newer version, I'll be investing in 2 of those as well.
> [ 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
>
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