Instructions
The Big Green
Ordinary Differential Equation Machine is a Java
applet that integrates systems of ordinary
differential equations and graphs the results.
The applet integrates with respect to the
variable "t" (often representing
"time"). Since any number of variables
may be entered into the Big Green Ordinary
Differential Equation Machine, it can be used to
model systems with an arbitrary number of
equations. For each variable, the user should
enter an intial value (value for t = 0) and a
derivative with respect to "t".
Input
AN IMPORTANT
NOTE: When you refresh or reload this page, all
input fields are reset.
Values entered
in the "Name:" and "Title:"
fields are for identification and do not affect
the numerical integration. The applet uses a
RungeKutta fixedstep method for the numerical
integration between the time entered in the
"Time Start:" field and the time
entered in the "Time End:" field. The
applet performs the integration using the
integral number of steps entered in the
"Number of Steps:" field. The applet
will also plot this many points. Make the value
high enough for accuracy, but as low as possible
for speed.
Variable names,
initial values, and time derivatives must be
entered in the large text area on the left.
Variable names can be of any length, but must
start with a letter. Capitalization is
significant ("a" is different from
"A"). The variable "t" is
reserved to represent time. The format for
entering variables is to enter one variable on
each line. Start the line with the variable name,
enter an equals sign (=) and then enter the
initial value of the variable. On the same line
then enter a comma (,), the variable name with a
prime ('), another equals sign, and then a
formula for the time derivative of the variable.
The formula can contain the any of following:
Operators:
+
for addition
 for subtraction
* for multiplication
/ for division
^ for power
Parentheses:
( )
Constants:
any number, e.g. 1.23, 6, 5.55E5
Variables:
any defined variable string



Valid Functions: ABS  absolute
value, ABS(x) = x
SQR  square, SQR(x) = x^{2}
EXP  exponential function, EXP(x) = e^{x}
LN  natural logarithm, LN(x) = log_{e}(x)
LOG10  base 10 logarithm, LOG10(x) = log_{10}(x)
SQRT  square root
SIN  sine
COS  cosine
TAN  tangent
ATN  arc tangent in the range of pi/2
to pi/2
INT  nearest integer

Controls
Pressing the
"Calculate" buttons starts the
integration and performs the plotting. The
"Update Plot" button will replot the
results of the integration. This can be used to
look at the behavior of different variables
without redoing the integration.
Output
The text area
below the plot gives feedback on any problems
with the input values and variables, or with
problems during the integration.
The values to be
plotted on the graph are controlled by the
"vertical" and "horizontal"
fields. The "vertical" field will
accept any number of defined, nonconstant
variables, each separated by a comma. The
horizontal field will accept only one defined,
nonconstant variable including "t".
©
2002 BPReid
