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International Journal of Mathematics and Mathematical Sciences
Volume 2011, Article ID 328197, 17 pages
Research Article

A Variable Step-Size Exponentially Fitted Explicit Hybrid Method for Solving Oscillatory Problems

Department of Mathematics, Faculty of Science, Universiti Putra Malaysia (UPM), Selangor, 43400 Serdang, Malaysia

Received 24 May 2011; Revised 9 September 2011; Accepted 9 September 2011

Academic Editor: Naseer Shahzad

Copyright © 2011 F. Samat 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.


An exponentially fitted explicit hybrid method for solving oscillatory problems is obtained. This method has four stages. The first three stages of the method integrate exactly differential systems whose solutions can be expressed as linear combinations of {1,x,exp(μx),exp(μx)},μC, while the last stage of this method integrates exactly systems whose solutions are linear combinations of {1,x,x2,x3,x4,exp(μx),exp(μx)}. This method is implemented in variable step-size code basing on an embedding approach. The stability analysis is given. Numerical experiments that have been carried out show the efficiency of our method.