Since I don't expect you want to learn UNIX and all the stuff that
goes along with it, all the information that I will give you here is
related to WINPP which you can download by
clicking the above link.
- If you don't have access to the internet, you can borrow a CD
with it in the library (4th floor). Copy the file:
windows/winpp/winpp.zip and uncompress it. I think Windows XP has
winzip compatibility built in. If you can't unzip it and you can't
download winpp.exe from the internet, please see me and I will put it
on a floppy.
- If you have the ZIP file, uncompress it and make a shortcut to
winpp.exe on your desktop.
- If you just downloaded the executable above, just leave it on the
- First create an ODE file
- Open a text editor, like Notepad (it is under Applications in
the Start Menu) or if you are really a masochist, Word.
- Type the following lines into it
# a generic first order equation with parameters
- Save the file as example1 in plain text ( DO NOT SAVE AS RTF
or DOC - It wont work )
- Now run and play with it
- Double click on winpp.exe and open your example1 file. If this
doesn't work, make a folder in My Computer C: and call it
myodes. Copy your example into this folder. Drag and drop it into
- You should see:
This is a phase-plane plot with the time-like variable, s
along the bottom and the variable y along the side. (You may
ask, why not put time itself along the bottom; this is because winpp
only does direction fields for 2-dimensional systems so we have to
fake it out.)
This file solves equations of the form
and you can change the f(y,s). The default is f(y,s)=y(1-y)
- Click on Phaseplane Grid parameters and change Dir. Fld.Grd to 20
- Click on Phasplane DirFld and direction fields will show up
- Click on Run Mouse and click somewhere in the plane. It will draw
a solution. Click on Run Mice and click al over the place. Click on
STOP to quit.
- Click on Edit Copy. Now it is saved to the clipboard and you can
paste it into a Paint or Word file to print out.
- Try plotting the directions fields for the more interesting model
- Click on Edit Edit RHS and click on the dY/dt box. Type in
y*(1-sin(t)-y) and then OK.
- Click on Ctrl E (Graphics Erase) and the on Phaseplane Dir Fld.
- Plot several trajectories using the Run Mice option
How do I ...
Finally some homework
- Draw direction fields for
- dy/dt = -y + .5*sin(y)
- dy/dt = -y + sin(y)
- dy/dt = -y + 2*sin(y)
- Try the following as well with a window |s|<2 and |y|<3; use
initial conditions y(0)=0, 2, -2. Do these seem to exist for all
values in the window?