A Numerical Integrator for Oscillatory Problems

Presented here is a numerical integrator, with sixth order of convergence, for solving oscillatory problems. Dispersion and dissipation errors are taken into account in the course of deriving the method. As a result, the method possesses dissipation of order infinity and dispersive of order six. Validity and effectiveness of the method are tested on a number of test problems. Results obtained show that the new method is better than its equals in the scientific literature.