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

Figure 9

The pendulum problem: Hamiltonian error using RK4 with is presented in (a), while (b) shows EH for BHTRKNM. We also solve the problem on a larger interval of integration , using the BHTRNM in (c) and (d) and the RK4 in (e) and (f), respectively.

(a) RK4-EH,

(b) BHTRKNM-EH, ;

(c) BHTRKNM, ;

(d) BHTRKNM-EH, ;

(e) RK4, ;

(f) RK4-EH, ;