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".
NOTE: When you refresh or reload this page, all
input fields are reset.
in the "Name:" and "Title:"
fields are for identification and do not affect
the numerical integration. The applet uses a
Runge-Kutta fixed-step 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
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:
- for subtraction
* for multiplication
/ for division
^ for power
any number, e.g. 1.23, -6, 5.55E-5
any defined variable string
ABS - absolute
value, ABS(x) = |x|
SQR - square, SQR(x) = x2
EXP - exponential function, EXP(x) = ex
LN - natural logarithm, LN(x) = loge(x)
LOG10 - base 10 logarithm, LOG10(x) = log10(x)
SQRT - square root
SIN - sine
COS - cosine
TAN - tangent
ATN - arc tangent in the range of -pi/2
INT - nearest integer
"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.
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, non-constant
variables, each separated by a comma. The
horizontal field will accept only one defined,
non-constant variable including "t".