Graphing Systems of D.E.s on the TI-82
-- a program --
The program is available in two formats.
A binary version that you can load directly
into the graphlink program and download to your calculator. NOTE:
If you have trouble downloading this, try holding the shift button on your
keyboard when you click on the link.
A screen shot for those typing in by hand.
Instructions for use:
The summary is below. Or you can see a worked-through
example with pictures of actual calculator displays.
- Enter your system as the opening screen instructs (halt the program
if you have already started it by pressing [QUIT]).
- Put dx/dt in terms of x, y, and t
in y1.
- Put dy/dt in terms of x, y, and t
in y2.
- Decide whether you want a graph of x vs. y, t
vs. x, or t vs. y.
- Set your window accordingly.
- Run the program.
- Input initial values for t, x, and y when asked.
- Input a final value for t and the number of steps desired.
- N=100 is often a good starting place.
- Increase or decrease the value of N to improve accuracy or
speed, respectively.
- When asked, indicate the axes you chose in (2).
Notes:
- When the program is done, you can type "T", "X",
and "Y" (and [ENTER]) to get the final values
of each.
- If you run the program a second time, you can input A and
B for the initial values of x, and y to keep the
previous values.
- You can use this for a single differential equation also, with accuracy
much better than a simple Euler's method. For example, to graph a solution
to the initial value problem dy/dx = 100-y, y(0) = 15:
- Translate to dy/dt = 100-y, y(0) = 15,
- Enter y1=0, y2=100-Y, and give the initial values
for t and y as 0 and 15 respectively.
- You can give anything at all (e.g. zero) for the inital value of x,
as it will be ignored. Similarly, y1 can be anything except
it must not be blank.
- Select "GRAPH T VS Y" and get your graph.
- The program uses a simple trapezoid or order-2 Runge-Kutta iteration.
Last modified April 30, 1997
Please mail comments or questions to: mjaneba
willamette.edu
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