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A coupled method of Laplace transform and Legendre wavelets for nonlinear Klein–Gordon equations
Author(s) -
Yin Fukang,
Song Junqiang,
Lu Fengshun
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2834
Subject(s) - legendre wavelet , mathematics , legendre polynomials , laplace transform , associated legendre polynomials , legendre's equation , legendre function , wavelet , mathematical analysis , nonlinear system , algebraic equation , wavelet transform , orthogonal polynomials , discrete wavelet transform , classical orthogonal polynomials , gegenbauer polynomials , physics , quantum mechanics , artificial intelligence , computer science
Klein–Gordon equation models many phenomena in both physics and applied mathematics. In this paper, a coupled method of Laplace transform and Legendre wavelets, named (LLWM), is presented for the approximate solutions of nonlinear Klein–Gordon equations. By employing Laplace operator and Legendre wavelets operational matrices, the Klein–Gordon equation is converted into an algebraic system. Hence, the unknown Legendre wavelets coefficients are calculated in the form of series whose components are computed by applying a recursive relation. Block pulse functions are used to calculate the Legendre wavelets coefficient vectors of nonlinear terms. The convergence analysis of the LLWM is discussed. The results show that LLWM is very effective and easy to implement. Copyright © 2013 John Wiley & Sons, Ltd.