|Main Window. This is an
exploration of the Duffing equation. The numerically computed
function trajectory is shown in white. Points in the plane are
colored according to which fixed point the system will converge when
started at that point.
|Stability Analysis of a
system of two linear ODEs. The green line is the known analytical
solution to the system. The white is the numerical solution
computed using the 4th order Runge-Kutta method. The stability
diagram shows the stability region for this method plotted in the
imaginary plane. The purple line corresponds to the primary
eigenvector (lambda) of the linear system, and the green spot shows the
location in the plane of timestep * lambda. The bigger the
timestep, the farther out that spot moves. When it leaves the
stability region, the method is no longer convergent. You can
click and drag on either the spot in the stability diagram or the
logarithmic slider in the main window to adjust the timestep and see how
the numerical solver's behaviour changes.
|You can visualize the vector
field with "ribbons" that use color and opacity gradients to depict the
general system behavior.
The list of Preset ODE systems is expanded so you can see all of the
systems that are built into Geode.
|You can type in any system you
want to to explore other ODEs besides the preset ones and to find out
how the various solvers work on them. You can define your own
parameters and use them in your equations. Text coloring lets you
know when you've entered a valid equation.