Cosine expansion‐based differential quadrature algorithm for numerical solution of the RLW equation

Dağ, İdris; Korkmaz, Alper; Saka, Bülent

doi:10.1002/num.20446

Cited by 21 publications

(4 citation statements)

References 27 publications

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“…Shu (2000) proposed the most general approach for finding the weighting coefficients by using Lagrange's interpolation as base functions. Recently, in literature the most frequently used differential quadrature procedures to solve one and two-dimensional differential equations are Lagrange interpolation polynomials-based differential quadrature method (PDQM), CDQM and other methods (Mittal and Jiwari, 2009, 2011Jiwari et al, 2012,a, b;Dag et al, 2010;Korkmaz, 2009;Korkmaz and Dağ, 2008;Korkmaz and Dağ, 2009a, b, c;Verma et al, 2014;Saka, 2009;Korkmaz, 2010;Shao and Wu, 2012;Dehghan and Nikpour, 2013b).…”

Section: Cdqmmentioning

confidence: 99%

Cosine expansion based differential quadrature algorithm for numerical simulation of two dimensional hyperbolic equations with variable coefficients

Verma

Jiwari

2015

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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Purpose – The purpose of this paper is to present the computational modeling of second-order two-dimensional nonlinear hyperbolic equations by using cosine expansion-based differential quadrature method (CDQM). Design/methodology/approach – The CDQM reduced the equations into a system of second-order differential equations. The obtained system is solved by RK4 method by converting into a system of first ordinary differential equations. Findings – The computed numerical results are compared with the results presented by other workers (Mohanty et al., 1996; Mohanty, 2004) and it is found that the present numerical technique gives better results than the others. Second, the proposed algorithm gives good accuracy by using very less grid point and less computation cost as comparison to other numerical methods such as finite difference methods, finite elements methods, etc. Originality/value – The author extends CDQM proposed in (Korkmaz and Dağ, 2009b) for two-dimensional nonlinear hyperbolic partial differential equations. This work is new for two-dimensional nonlinear hyperbolic partial differential equations.

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Section: Cdqmmentioning

confidence: 99%

Cosine expansion based differential quadrature algorithm for numerical simulation of two dimensional hyperbolic equations with variable coefficients

Verma

Jiwari

2015

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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“…Benjamin et al [2] showed the similarity of wave solutions of the RLW equation to the wave solutions of the more widely known Korteweg-de Vries (KdV) equation. RLW equation has been solved by various numerical method including finite difference method [3][4][5], collocation method [7][8][9][10][11][12], Galerkin method [13][14][15][16][17][18][19][20][21][22], and Quadrature method [23,24].…”

Section: Introductionmentioning

confidence: 99%

Cubic B-Spline Quasi-Interpolation Method For Regularized Long Wave Equation

Irk¹,

Mersin²

2018

Journal of Engineering Technology and Applied Sciences

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In this study, we present a numerical method to solve the Regularized Long Wave (RLW) equation, based on cubic B-spline quasi-interpolation for the space integration and Crank-Nicolson method for the time integration. The method is tested on the problems of propagation of a solitary wave and interaction of two solitary waves. The three conservation quantities of the motion are calculated to determine the conservation properties of the proposed algorithm.

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“…The Adomian decomposition method is another method to design some of the exact solitary wave solutions of the generalized form of the BBM equation [6]. Besides the analytical and exact solutions of the BBM equation, many numerical techniques from different families are developed and implemented for the numerical solutions to various evolution problems for the BBM equation [7,8,9]. The symmetric BBM equation is defined by Seyler and Fenstermacher [10] to describe ion acoustic and space charge waves in the weakly nonlinear sense.…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions to Some Conformable Time Fractional Equations in Benjamin-Bona-Mahony Family

Korkmaz¹

2016

Preprint

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The conformable time fractional forms of some partial differential equations are solved in the study. The existence of chain rule and the derivative of composite function enable the equations to be reduced to some ordinary differential equations by using some particular wave transformations. The modified Kudryashov method implemented to derive the exact solutions for the Benjamin-Bona Mahony (BBM), the symmetric BBM and the equal width (EW) equations in the conformable fractional time derivative forms. The obtained explicit solutions are illustrated for some time fractional orders in the interval (0, 1].

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Cosine expansion‐based differential quadrature algorithm for numerical solution of the RLW equation

Cited by 21 publications

References 27 publications

Cosine expansion based differential quadrature algorithm for numerical simulation of two dimensional hyperbolic equations with variable coefficients

Cosine expansion based differential quadrature algorithm for numerical simulation of two dimensional hyperbolic equations with variable coefficients

Cubic B-Spline Quasi-Interpolation Method For Regularized Long Wave Equation

Exact Solutions to Some Conformable Time Fractional Equations in Benjamin-Bona-Mahony Family

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