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Geode is a visualization tool for understanding ordinary differential equations and the algorithms that are used to solve them on computers.  With it, you can:
  • type in any system of two ODEs (including non-autonomous systems) or select one of several interesting preconfigured systems
  • numerically integrate an ODE system using one of several standard ODE solvers, including 4th-order Runge-Kutta and the backward Euler method.
  • for linear ODEs, compare the numerical result to the analytical solution
  • explore the stability properties of various ODE solvers in an interactive visualization of their imaginary plane stability regions
  • visualize the convergence behavior of non-linear ODE systems under various solvers with a convergence-point-based coloring of the plane
  • save and load ODE systems and settings
We expect that Geode will be useful for students of numerical analysis who would like to gain a better understanding of the behavior of systems of ordinary differential equations and their solvers.

Questions?  Bugs?
Jeff Klingner (klingner at or Dave Akers (dakers at