Two-step explicit methods for second-order IVPs with oscillatory solutions

Abstract

In this paper, we present a class of non-conventional two-step explicit methods for solving the second-order initial value problems (IVPs) with periodic or oscillatory solutions. The methods have second algebraic order, a large interval of periodicity 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:

• periodic initial value problem
• P-stability
• interval of periodicity
• phase-lag
• vector product and quotient

2000 AMS Subject Classification :

• 65L05

Acknowledgements

This work was partially supported by NNSF of China (no. 10771099) and Jiangsu Planned Projects for Postdoctoral Research Funds (no. 0701039C). The author is grateful to the anonymous referees and Professor Xinyuan Wu for their helpful suggestions.