A collection of explicit Runge-Kutta methods of various orders
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of different orders, along with a couple of programs to exercise them.
Build and run testrk, volterra, volterra2, and arenstorf:
o testrk exercises all of the methods in a non-adaptive way,
solving a test problem with a known analytic solution,
to check convergence. (This was what first indicated that
there was a problem with the Fehlberg 7(8) listing in HNW.)
o volterra uses a non-adaptive method to solve the Lotka-Volterra
equations from t=0 to t=40: either from a built-in starting point,
or from a starting point specified on the command line.
o volterra2 does the same, except it uses an adaptive solver
o arenstorf solves the restricted 3-body problem (earth+moon+satellite)
using an adaptive solver with some specific initial conditions
which yield periodic orbits
The volterra2 and arenstorf examples use an "oracle" function to
decide what is a good step size. Right now that oracle function is in
each test file; arguably it should be in the RungeKutta module.
Eventually it will be, but I haven't spent much time yet on making
that oracle especially good.