An important equation of nonlinear mechanics is van der Pol's equation,
for . For any initial conditions, the solution of this equation converges to a unique periodic solution, called a stable limit cycle. This code uses RKSUITE to solve this problem with , , for . The code is followed by a tabulation of the solution at and a plot of the solution in the phase plane: .
To put this problem in a form suitable for RKSUITE, we let , to obtain the equivalent system:
The system of ODEs is implemented in the subroutine F. The code uses the (4,5) Runge-Kutta pair.
Figure 5: The van der Pol equation.
(See exercise set 3.)