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
,
Xiao-Qun Cao
- National University of Defense Technology, Changsha, P.R. China
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.
Keywords
- Picard iteration method
- legendre wavelets
- IVPS
- nonlinear
How to 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. https://doi.org/ 10.7763/IJAPM.2013.V3.190
Copyright & License
Copyright © 2013 by the authors. 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 (CC BY 4.0).