2013
DOI: 10.1002/mma.2834
|View full text |Cite
|
Sign up to set email alerts
|

A coupled method of Laplace transform and Legendre wavelets for nonlinear Klein-Gordon equations

Abstract: 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 a… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
4
1

Citation Types

0
13
0

Year Published

2014
2014
2021
2021

Publication Types

Select...
4
4

Relationship

0
8

Authors

Journals

citations
Cited by 31 publications
(13 citation statements)
references
References 42 publications
0
13
0
Order By: Relevance
“…This method has been systematically studied for linear partial differential equations [1,12,13,21,22], however very few works have been done to solve nonlinear partial differential equations [3][4][5]. It is also observed that the operational matrix wavelet methods for the non linear partial differential equations in the recent literature fall into two groups: methods for initial value problems [14,24] and the methods for initial and boundary value problems [3][4][5][6]15,17]. By assuming the existence and uniqueness of solution as well as the convergence of the quasilinearization scheme, classical quasilinearization based operational matrix wavelet method for various types of ordinary and partial differential equations are studied in [7][8][9][17][18][19] and [3,5,6,10,15], respectively.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…This method has been systematically studied for linear partial differential equations [1,12,13,21,22], however very few works have been done to solve nonlinear partial differential equations [3][4][5]. It is also observed that the operational matrix wavelet methods for the non linear partial differential equations in the recent literature fall into two groups: methods for initial value problems [14,24] and the methods for initial and boundary value problems [3][4][5][6]15,17]. By assuming the existence and uniqueness of solution as well as the convergence of the quasilinearization scheme, classical quasilinearization based operational matrix wavelet method for various types of ordinary and partial differential equations are studied in [7][8][9][17][18][19] and [3,5,6,10,15], respectively.…”
Section: Introductionmentioning
confidence: 99%
“…(1.1) represents various mathematical models in mathematical biology, plasma physics and quantum mechanics, to name a few. Considerable attention has been directed towards the development numerical scheme for partial differential equation using operational matrix wavelet methods [1,[3][4][5][12][13][14]21,22,24]. This method has been systematically studied for linear partial differential equations [1,12,13,21,22], however very few works have been done to solve nonlinear partial differential equations [3][4][5].…”
Section: Introductionmentioning
confidence: 99%
“…G. Hariharan, R. Rajaraman [137] had solved a few reaction-diffusion problems by the Laplace Legendre wavelets method. Yin et al [138,139] introduced the Laplace Legendre wavelets method for solving Klein-Gordon and Lane-Emden-Type Differential Equations. Recently, Hariharan and Kannan [140] reviewed the Haar wavelets for solving differential and integral equations arising in science and engineering.…”
Section: Function Approximationmentioning
confidence: 99%
“…In recent years, many analytical/approximation methods have been proposed for solving Fisher's and fractional Fisher's equations. For example, Adomian decomposition method [15], the variational iteration method [16], the Homotopy perturbation method [13,17], the differential transform method [2], the homotopy analysis method [24,26], and other methods [1,3,18,27]. Recently, Hariharan and Rajaraman [9] established a new coupled wavelet-based method applied to the nonlinear reaction-diffusion equation arising in mathematical chemistry.…”
Section: Introductionmentioning
confidence: 99%