A new Legendre wavelets decomposition method for solving PDEs

Naima Ablaoui-Lahmar; Omar Belhamiti; Sidi Mohammed Bahri

doi:10.26637/mjm201/009

Abstract

In this paper, we present a novel technique based on the Legendre wavelets decomposition. The properties of Legendre wavelets are used to reduces the PDEs problem into the solution of ODEs system. To illustrate our results, two examples are studied using a special software package which implements the proposed algorithms.

Keywords:

Legendre Wavelets, Legendre Polynomials, Operational Matrix of integration, Telegraph Equation

Mathematics Subject Classification:

49M37, 30E25

Authors Imprint References Funding Related Articles Downloads

Naima Ablaoui-Lahmar Department of Mathematics and Computer Science, Abdelhamid Ibn Badis University, Mostaganem 27000, Algeria.
Omar Belhamiti Department of Mathematics and Computer Science, Abdelhamid Ibn Badis University, Mostaganem 27000, Algeria. https://orcid.org/0000-0002-6514-2769
Sidi Mohammed Bahri Department of Mathematics and Computer Science, Abdelhamid Ibn Badis University, Mostaganem 27000, Algeria.

Pages: 72-81
Date Published: 01-01-2014
Vol. 2 No. 01 (2014): Malaya Journal of Matematik (MJM)

R. Dautray and J.-L. Lions: Mathematical Analysis and Numerical Methods for Science and Technology. Vol. 8: Evolution : semi-groupe, variationnel, édition Masson, 1980.

Jafari, S.A. Yousefi, M.A. Firoozjaee, S. Momanic, C.M. Khalique dApplication of Legendre wavelets for solving fractional differential equations, Computers and Mathematics with Applications 62 (2011) 1038–1045[5] DOI: https://doi.org/10.1016/j.camwa.2011.04.024

F. Mohammadi, M.M.Hosseini : A new Legendre wavelet operational matrix of derivative and its applications in solving the singular ordinary differential equations, Journal of the Franklin Institute 348 (2011), 1787–1796 DOI: https://doi.org/10.1016/j.jfranklin.2011.04.017

Mujeeb ur Rehman, Rahmat Ali Khan : The Legendre wavelet method for solving fractional differential equations, Commun Nonlinear Sci Numer Simulat 16 (2011) 4163–4173. DOI: https://doi.org/10.1016/j.cnsns.2011.01.014

Razzaghi M, Yousefi S. : Legendre wavelets direct method for variational problems.Mathematics and Computers in Simulation, 53, 2000, 185-192. DOI: https://doi.org/10.1016/S0378-4754(00)00170-1

Mohsen Razzaghi and Sohrabali Yousefi : Legendre wavelets method for constrained optimal control problems, Mathematical Methods in the Applied Sciences, 25:529–539, 2002. DOI: https://doi.org/10.1002/mma.299

Razzaghi M, Yousefi S. The Legendre wavelets operational matrix of integration. International Journal of Systems Science 2001; 32:495–502. DOI: https://doi.org/10.1080/00207720120227

M.Tavassoli Kajani,A.Hadi Vencheh :Solving linear integro-differential equation with Legendre wavelets.International Journal of Computer Mathematics 81, 2004, 719-726. DOI: https://doi.org/10.1080/00207160310001650044

S.G. Venkatesh , S.K. Ayyaswamy, S. Raja Balachandar : The Legendre wavelet method for solving initial value problems of Bratu-type, Computers and Mathematics with Applications 63 (2012) 1287–1295 DOI: https://doi.org/10.1016/j.camwa.2011.12.069

Sohrab Ali Yousefi : Numerical solution of Abel’s integral equation by using Legendre wavelets, Applied Mathematics and Computation 175 (2006) 574–580. DOI: https://doi.org/10.1016/j.amc.2005.07.032

Xiao-Yang Zheng, Xiao-Fanyang, Young Wu. :Technique for solving differential equation by extended Legendre wavelets.International Conference on wavelet analysis and Pattern Recognition,Hong kong Proceed. , 2008, 30-31. DOI: https://doi.org/10.1109/ICWAPR.2008.4635863

Xiaoyang Zheng and Xiaofan Yang : Techniques for solving integral and differential equations by Legendre wavelets, International Journal of Systems Science Vol. 40, No. 11, November 2009, 1127–1137 DOI: https://doi.org/10.1080/00207720902974710