Euler's method on the TI82/83
Given a differential equation, say y' = 3xy, here is how
to make the TI82/83 draw an Euler's method solution for that differential
equation.

We must translate the differential equation: In place of the function (y
in
this case), write Y (upper case), in place of y'
write Y1, and in place of the variable (x in this
case), write X. So we get
Y1=3XY.

Now press [Y=] and enter our differential equation from
the last step on the first line:

Press [WINDOW] to select a suitable window or range. Here's
what I've picked:

Press [PRGM] and select the EULER program.
Press [ENTER]once to paste prgmEULER on
your text screen; press [ENTER] again to run the program.

Remember that Euler's method requires an initial condition or starting
point for a solution curve. Suppose, for examples, that the desired
initial condition was y(1) = 4. When the program begins, you must
input that initial condition as follows:

When the program asks "X START?", give the xcoordinate
of the initial condition. In our example y(1) = 4, X
START would be 1.

When the program asks "Y START?", give the ycoordinate
of the initial condition. In our example y(1) = 4, Y START
would be 4.

Euler's method can run forever; you must tell the program when to stop.
If you want a solution curve from X START (1 in the above
example) to, say, 5, you would give "5" for "FINAL X".

Finally, give the number of steps desired (so the stepsize works
out to be (FINAL X  X START)/(# of steps) ).

Your screen will look something like this before you press [ENTER]
the
last time:

When you press [ENTER] the last time, the calculator graphs
an approximate solution curve to the differential equation, for the given
initial condition:

You can get the coordinates of the last point plotted by typing X
[ENTER] [ALPHA] Y [ENTER]:
A more accurate differential equations
solution grapher is available. It is similar to the better methods
built in to the TI85/86, though not quite as sophisticated. It will generally
require far fewer steps for far greater accuracy.
Last Modified December 8, 1998.
Prof.
Janeba's Home Page  Send comments or questions to: mjanebawillamette.edu
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