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- Errors in ODE integration schemes as a function of
method and step size. Empirical measures of the order of a method.
- Experiment with graphical integrators and then argue
for the correctness of some of the results seen. (e.g. fences,
vertical asymptotes, behavior at infinity.)
- Bifurcations of 2d homogeneous linear systems.
- Matrix exponential and applications.
- Computer assistance for variation of parameters.
- Computer assistance for change of coordinates.
- Logistic, predator-prey and generalizations as a
function of parameter.
- Computer algebra systems in scratchpad mode to
assist with power series and Frobenius methods solutions.
- Use computers to bring some special functions to life.
- Study some basic low codimension bifurcations (e.g.
saddle node, pitchfork, hopf.)
- Sensitive dependence on initial conditions.
- Study attractive periodic points as a function of
parameter in the 1d discrete logistic equation to see chaotic behavior.
- Explore the restricted 3 body problem numerically.
- Web Resources:
- Java and Matlab versions of Dfield and Pplane:
- Dynamics Solver Source:
- Interactive Differential Equations:
- http://awlonline.com/ide/ (All labs available online in pdf