**pendulum_nonlinear_exact_test**,
a MATLAB code which
calls pendulum_nonlinear_exact(), which
evaluates an exact formula for the solution of the
the ordinary differential equations (ODE) that represent
the behavior of a nonlinear pendulum of length L under a
gravitational force of strength G.

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

pendulum_nonlinear_exact, a MATLAB code which evaluates an exact formula for the solution of the the ordinary differential equations (ODE) that represent the behavior of a nonlinear pendulum of length L under a gravitational force of strength G.

- pendulum_nonlinear_exact_test.m, calls all the tests.
- pendulum_nonlinear_exact_test.sh, runs all the tests.
- pendulum_nonlinear_exact_test.txt, the output file.

- midpoint.m, solves an ODE using the (implicit) midpoint method.
- pendulum_nonlinear_midpoint.m, compares the exact solution to a solution produced by midpoint().
- pendulum_nonlinear_midpoint_energy.png, a plot of the energy of the nonlinear pendulum behavior over time.
- pendulum_nonlinear_midpoint_phase.png, the phase plot.
- pendulum_nonlinear_midpoint_theta.png, a plot of the the angular deflection over time.
- pendulum_nonlinear_midpoint_thetadot.png, a plot of the angular velocity over time.

- pendulum_nonlinear_ode23.m, compares the exact solution to a solution produced by ode23().
- pendulum_nonlinear_ode23_energy.png, a plot of the energy of the nonlinear pendulum behavior over time.
- pendulum_nonlinear_ode23_phase.png, the phase plot.
- pendulum_nonlinear_ode23_theta.png, a plot of the the angular deflection over time.
- pendulum_nonlinear_ode23_thetadot.png, a plot of the angular velocity over time.