A Trigonometrically Fitted Block Method for Solving Oscillatory Second-Order Initial Value Problems and Hamiltonian Systems

Figure 8

The pendulum problem: phase diagrams for BHTRKNM with are presented in (a), (b), and (c), respectively. (d) illustrates a distortion in the flow for the RK4, while (e) shows exact flow of the pendulum problem. In the diagrams, ; .

(a) BHTRKNM, ;

(b) BHTRKNM, ;

(c) BHTRKNM, ;

(d) RK4,

(e) Exact flow