Alkahest III: automatic analysis of periodic weakly nonlinear ODEs

In previous papers by the current authors various attempts that have been made in the automatic derivation of periodic solutions to weakly nonlinear differential equations have been reported. The equations in question are all perturbations of y′+y = 0, related to the equations that occur in the study of celestial mechanics. In the current paper the analysis of these equations has been taken further, with the automatic system, named Alkahest III, being able to determine the solution to equations even when the user's initial conditions are invalid. The system can produce an approximate solution itself, and there are facilities to write an algebra program for REDUCE or CAMAL to generate higher order solutions.