next up previous

2.2.5 RKSUITE Example

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.)