One-step explicit methods for the numerical integration of perturbed oscillators

Abstract

In this paper, we present a class of one-step explicit zero-dissipative nonlinear methods for the numerical integration of perturbed oscillators, which have second algebraic order and high phase-lag order. For multi-dimensional problems, we give the vector form of the methods with the aid of a special vector operation. Some numerical results are reported to illustrate the efficiency of our methods.

Keywords:

• perturbed oscillators
• interval of periodicity
• phase-lag error
• one-step explicit methods
• vector product and quotient

2010 AMS Subject Classification :

• 65L05

Acknowledgements

This work was supported by NSF of Universities of Anhui Province, China (No. KJ2010A248) and Scientific Research Start-up Fund of Chuzhou University, China (No. 2010qd03).