2018
DOI: 10.1080/16583655.2018.1515324
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Laguerre wavelets collocation method for the numerical solution of the Benjamina–Bona–Mohany equations

Abstract: In this paper, a new approach for the accurate numerical solution of the Benjamin-Bona-Mahony (BBM) equations with the initial and boundary conditions using Laguerre wavelets is presented. This method is based on the truncated Laguerre wavelet expansions used to convert the initial and boundary value problems into systems of algebraic equations which can be efficiently solved by suitable solvers. Illustrative examples are included to demonstrate the validity and applicability of the technique. Numerical result… Show more

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Cited by 56 publications
(16 citation statements)
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“…Wavelet sanctions the precise depiction of a variety of functions and operators [14,15]. Recently, many research papers are published on different types of wavelets, the aim of these research papers to provide the numerical solutions to differential equations of integer order as well as fractional order with the aid of wavelets [16][17][18][19][20][21]. Recently, Boonrod and Razzaghi discussed a numerical approach based on Legendre wavelets for examining fractional differential equations (FDEs) by the exact formula for Riemann-Liouville (RL) [22].…”
Section: Introductionmentioning
confidence: 99%
“…Wavelet sanctions the precise depiction of a variety of functions and operators [14,15]. Recently, many research papers are published on different types of wavelets, the aim of these research papers to provide the numerical solutions to differential equations of integer order as well as fractional order with the aid of wavelets [16][17][18][19][20][21]. Recently, Boonrod and Razzaghi discussed a numerical approach based on Legendre wavelets for examining fractional differential equations (FDEs) by the exact formula for Riemann-Liouville (RL) [22].…”
Section: Introductionmentioning
confidence: 99%
“…The fractional calculus has been extended extremely and investigated in distinct areas and applications by many research works (see, for example, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]). In 1937, Fisher, Kolmogorov, Petrovsky, and Piscounov investigated independently the Fisher-KPP equation (or Fisher's equation; see [21,22]).…”
Section: Introductionmentioning
confidence: 99%
“…Wavelet is a small wave that oscillates in the small domain and vanishes elsewhere, also, we treat this as a function generated by a small function called mother wavelet. Many researchers developed numerical methods using wavelets as follows, Laguerre wavelets collocation method [17], CAS wavelets analytic solution [18], Hermite wavelets operational matrix method [16], Theoretical study on continuous polynomial wavelet [15], Haar wavelet collocation method [10], Two-dimensional Legendre wavelets [6], etc.…”
Section: Introductionmentioning
confidence: 99%