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Journal of Applied Mathematics
Volume 2013, Article ID 591636, 5 pages
Research Article

A Legendre Wavelet Spectral Collocation Method for Solving Oscillatory Initial Value Problems

1Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Selangor, Malaysia
2Department of Mathematics, University Putra Malaysia, 43400 Serdang, Selangor, Malaysia
3Department of Mathematics, Khorasgan Branch, Islamic Azad University, Khorasgan, Isfahan, Iran
4School of Mathematical Sciences, National University of Malaysia (UKM), 43600 Bangi, Selangor, Malaysia

Received 26 January 2013; Revised 15 April 2013; Accepted 15 April 2013

Academic Editor: Srinivasan Natesan

Copyright © 2013 A. Karimi Dizicheh 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.


In this paper, we propose an iterative spectral method for solving differential equations with initial values on large intervals. In the proposed method, we first extend the Legendre wavelet suitable for large intervals, and then the Legendre-Guass collocation points of the Legendre wavelet are derived. Using this strategy, the iterative spectral method converts the differential equation to a set of algebraic equations. Solving these algebraic equations yields an approximate solution for the differential equation. The proposed method is illustrated by some numerical examples, and the result is compared with the exponentially fitted Runge-Kutta method. Our proposed method is simple and highly accurate.