LaPlace Transforms in TI89 and HP48 compared by Perez-Franco

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LaPlace Transforms in TI89 and HP48 compared by Perez-Franco

[ 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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