Fourier Cosine Differential Quadrature Method for Beam and Plate Problems

Shao, Wen Ting; Wu, Xiong Hua

doi:10.4028/www.scientific.net/amm.138-139.699

Cited by 1 publication

(1 citation statement)

References 6 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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