Volume 3 Number 2 (Mar. 2013)
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IJAPM 2013 Vol.3(2): 127-131 ISSN:2010-362X
DOI: 10.7763/IJAPM.2013.V3.190

Legendre Wavelets-Picard Iteration Method for Solution of Nonlinear Initial Value Problems

Fu-Kang Yin, Wang-Yi Han, Jun-Qiang Song, and Xiao-Qun Cao

Abstract—Numerical methods for solving initial value problems (IVPs) are of fundamental importance for analyzing and controlling dynamic systems. In this paper, we first present a new Legendre wavelets-Picard iteration method (LWPIM) for solving IVPs. Combining Legendre wavelets method with Picard iteration method, LWPIM iteratively refines estimates of the solutions until the iteration converges and can avoid the solution of a system of algebraic equations. Furthermore, the developed vector-matrix form makes MCPI methods computationally efficient. Numerical results show that the proposed method is mathematically simple and easy to implement while still keeps the high accuracy.

Index Terms—Picard iteration method, legendre wavelets, IVPS, nonlinear.

The authors are with National University of Defense Technology, Changsha, P.R. China (e-mail: yinfukang@nudt.edu.cn, hanwangyige@163.com, junqiang@nudt.edu.cn, caoxiaoqun@nudt.edu.cn).

 

Cite: Fu-Kang Yin, Wang-Yi Han, Jun-Qiang Song, and Xiao-Qun Cao, "Legendre Wavelets-Picard Iteration Method for Solution of Nonlinear Initial Value Problems," International Journal of Applied Physics and Mathematics  vol. 3, no. 2, pp. 127-131, 2013.

General Information

ISSN: 2010-362X (Online)
Abbreviated Title: Int. J. Appl. Phys. Math.
Frequency: Quarterly
DOI: 10.17706/IJAPM
Editor-in-Chief: Prof. Haydar Akca 
Abstracting/ Indexing:  Index Copernicus, EI (INSPEC, IET), Chemical Abstracts Services (CAS), Nanowerk Database, Google Scholar, EBSCO, etc.
E-mail: ijapm@iap.org
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