# Two Point Boundary Value Problems

This form allows you to create a Java applet to plot solutions to a system of two differential equations. Applet names must not contain any spaces or special characters. There are no length restrictions. Both upper and lower case characters are permitted, as are numbers.

Name of the applet

Enter the names and initial values of up to four parameters (optional).
Name: Value:
Name: Value:
Name: Value:
Name: Value:

Enter the differential equations. They should be in the format e.g.
x'=2*y^2-sin(y)
y'=-alpha*x
You may select the color with which the orbits will be drawn in the selection box to the right of the text area for the first equation.

There are more things that you may enter below, but they are all optional. If you wish to change display bounds or plot a function along with the orbits of the differential equations, then fill in fields below, and return to the following "Submit" button.

Note that you will have to change the name of your applet if this is a second submission. Netscape caches Java applets, and cannot be made to load the same applet a second time. Thus if you are modifying your existing applet, you will need to give the modified applet a new name.

Enter the lower and upper bounds for the independent (time) variable.

Lower Bound: Upper Bound:

Enter the lower and upper bounds for the first dependent variable.

Lower Bound: Upper Bound:

Enter the lower and upper bounds for the second dependent variable.

Lower Bound: Upper Bound:

Next, enter the functions you want to plot. These allow you to plot nullclines, for example. Observe that the independent variable is always called "t". The usual complement of intrinsic functions are available. In addition, the heaviside function is available, i.e. heaviside(t)=0 if t<0, and =1 if t>0. The following are examples of acceptable function entries.
tom(t)=t^2+1
dick(t)=sin(2*t)
harry(t)=heaviside(t-2)+exp(-2*t)
The following are unacceptable function entries.
t^2+1
f(x)=sin(2*x)
harry=4 Each function you enter must have a different name. For each function you enter, you may specify a color.

Put the desired step size for the algorithm in here: