Our θ approximations are substituted in, and our θ˙ RKF45 approximation is subtracted from this value. From this equation, the period T of the problem is approximated when the conditions for periodicity are satisfied, namely using the equation
where θmin and θmax are the two closest values for which θ˙=0. T is calculated using Chebyshev-Gauss quadrature (Simpson's rule could not be used as there are unremovable singularities at the endpoints which makes Simpson's rule markedly less accurate).
Information
Data
Notes
T:
Period of the problem, auto-calculated.
θmin
The value of θmin used in the above period equation.
θmax
The value of θmax used in the above period equation.
RKF45 step number
Number of steps used in our Runge-Kutta-Fehlberg approximation of the solution.