ODE Workbench

ODE Workbench

Variable =   Value =   Rate =

Equation # =

Press the add button after you enter the values for each equation.  Create the system after all equations have been entered. The variables used to define the first two rate equations will be plotted on the horizontal and vertical axes, respectively.  For example, the rate equations for radioactive decay can be scripted as follows:

Variable Initial Value Rate
t 0 1
n 100 -0.1*n

The time variable will usually have a rate of unity since dt/dt=1.  The initial number of radioactive particles is set to 100.  Approximately 10% of these particles will decay during every time unit.

Second order ODEs can be rewritten as a coupled system of first order differential equations.  For example, the system of differential equations that describe a simple harmonic oscillator can be written as:

Variable Initial Value Rate
t 0 1
x 1 v
v 0 -2*x

The graph will display x(t) if the equations are entered in the same order as they appear in the table.  Reverse the order of the last two equations to display v(t).