Abstract and Applied Analysis
Volume 2012 (2012), Article ID 742585, 15 pages
http://dx.doi.org/10.1155/2012/742585
Research Article

New Phase Fitted and Amplification Fitted Numerov-Type Methods for Periodic IVPs with Two Frequencies

Yonglei Fang,1 Xiong You,2 and Zhaoxia Chen2

1School of Mathematics and Statistics, Zaozhuang University, Zaozhuang 277160, China
2Department of Applied Mathematics, Nanjing Agricultural University, Nanjing 210095, China

Received 8 April 2012; Revised 20 June 2012; Accepted 28 August 2012

Academic Editor: Josip E. Pecaric

Copyright © 2012 Yonglei Fang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Phase fitted and amplification fitted Numerov-type methods for periodic initial value problems with two frequencies are investigated. A one-frequency method and a two-frequency method are constructed. The two new methods both have algebraic order five and are dispersive of order six and dissipative of order five. The two-dimensional absolute stability region for the one-frequency method and the three-dimensional absolute stability region for the two-frequency method are plotted. Numerical experiments are reported to show the efficiency and competence of the two new methods.