Explicit Computation of Weighting Coefficients in the Harmonic Differential Quadrature

Chen, Shu; Xue, Hansong

doi:10.1006/jsvi.1996.0894

Cited by 117 publications

(70 citation statements)

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“…Determining the weight coefficients is the most crucial step in the use of DQM. Shu and Xue (1997) worked on the selection of the weight coefficients and proposed several solutions in their studies. The weight coefficients change upon approximation function and according to the chosen approximation function, the method takes different names such as Polynomial Differential Quadrature, Fourier Expansion Base Differential Quadrature and Harmonic Differential Quadrature (Civalek, 2004;Shu et al, 2002).…”

Section: Differential Quadrature Methodsmentioning

confidence: 99%

Differential Quadrature Method for Linear Long Wave Propagation in Open Channels

Kaya¹,

Arisoy²

2010

Wave Propagation in Materials for Modern Applications

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Section: Differential Quadrature Methodsmentioning

confidence: 99%

Differential Quadrature Method for Linear Long Wave Propagation in Open Channels

Kaya¹,

Arisoy²

2010

Wave Propagation in Materials for Modern Applications

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“…In DQM, the weighting coefficients are computed by using several kinds of test functions: spline function, sinc function, Lagrange interpolation polynomials and Legendre polynomials [14][15][16][17][18][19][20] etc. This section redescribes MCB-DQM [13] to complete our problem.…”

Section: Description Of Mcb-dqmmentioning

confidence: 99%

A Novel Approach for Numerical Computation of Fokker-Planck Equation

Kumar¹,

Singh²,

Nath³

2016

JMSS

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This paper present an implementation of "modified cubic B-spline differential quadrature method (MCB-DQM)" proposed by Arora & Singh (Applied Mathematics and Computation Vol. 224(1) (2013) 161-177) for numerical computation of Fokker-Planck equations. The modified cubic B-splines are used as set of basis functions in the differential quadrature to compute the weighting coefficients for the spatial derivatives, which reduces Fokker-Planck equation into system of first-order ordinary differential equations (ODEs), in time. The well known SSP-RK43 scheme is then applied to solve the resulting system of ODEs. The efficiency of proposed method has been confirmed by three examples having their exact solutions. This shows that MCB-DQM results are capable of achieving high accuracy. Advantage of the scheme is that it can be applied very smoothly to solve the linear or nonlinear physical problems, and a very less storage space is required which causes less accumulation of numerical errors.

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“…In this regard a great work is done by Shu and Richard (1992). Further Shu and Chew (1997), Shu (2000), and Shu and Xue (1997) proposed easy algebraic formulations to determine weighting coefficients of first and second order derivatives when the function is approximated by a Fourier series expansion.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of generalized Burger’s-Huxley equation using local radial basis functions

Bukhari¹,

Arshad

Batool

et al. 2017

Int. j. adv. appl. sci

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Explicit Computation of Weighting Coefficients in the Harmonic Differential Quadrature

Cited by 117 publications

References 0 publications

Differential Quadrature Method for Linear Long Wave Propagation in Open Channels

Differential Quadrature Method for Linear Long Wave Propagation in Open Channels

A Novel Approach for Numerical Computation of Fokker-Planck Equation

Numerical solution of generalized Burger’s-Huxley equation using local radial basis functions

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