Shock wave simulations using Sinc Differential Quadrature Method

Korkmaz, Alper; Dağ, İdris

doi:10.1108/02644401111154619

Cited by 114 publications

(78 citation statements)

References 39 publications

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“…A technique based on modified cubic B-spline is proposed to find the weighting coefficients rather than using the traditional method of Lagrange interpolation [7]. 2.…”

Section: Resultsmentioning

confidence: 99%

“…Nowadays, most frequently used quadrature methods are based on sine-cosine expansion and Lagrange interpolation. Korkmaz and Dag [7,8] have used cosine expansion-based differential quadrature method and sine differential quadrature method for many nonlinear partial differential equations. Mittal et al [9][10][11][12] proposed polynomial-based differential quadrature method for numerical solutions of nonlinear partial differential equations.…”

Section: Description Of Modified Cubic B-spline Differential Quadratumentioning

confidence: 99%

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Numerical Solutions of Differential Equations Using Modified B-spline Differential Quadrature Method

Mittal

Dahiya

2015

Springer Proceedings in Mathematics &Amp; Statistics

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In this article, a modified cubic B-spline differential quadrature method (MCB-DQM) is proposed to solve some of the basic differential equations. Here we have considered an ordinary differential equation of order two along with heat equation and one-and two-dimensional wave equations. A nonlinear ordinary differential equation of order two is also considered. The ordinary differential equation is reduced to a system of nonhomogeneous linear equations which is then solved by using the Gauss elimination method, whereas the heat equation and the one-dimensional and two-dimensional heat and wave equations are reduced to a system of ordinary differential equations. The system is then solved by the optimal four-stage three-order strong stability preserving time stepping Runge-Kutta (SSP-RK43) scheme. The reliability and efficiency of the method have been tested on six examples. Keywords

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“…A technique based on modified cubic B-spline is proposed to find the weighting coefficients rather than using the traditional method of Lagrange interpolation [7]. 2.…”

Section: Resultsmentioning

confidence: 99%

Section: Description Of Modified Cubic B-spline Differential Quadratumentioning

confidence: 99%

Numerical Solutions of Differential Equations Using Modified B-spline Differential Quadrature Method

Mittal

Dahiya

2015

Springer Proceedings in Mathematics &Amp; Statistics

View full text Add to dashboard Cite

show abstract

“…Nowadays, most frequently used quadrature methods are based on sine-cosine expansion and Lagrange interpolation. Korkmaz and Dag [20,21] have used cosine expansion based differential quadrature method and sinc differential quadrature method for many nonlinear partial differential equations. Mittal et al [22][23][24][25] proposed the polynomial based differential quadrature method for numerical solutions of nonlinear partial differential equations.…”

Section: Description Of Modified Cubic B-spline Differential Quadratumentioning

confidence: 99%

Numerical simulation on hyperbolic diffusion equations using modified cubic B-spline differential quadrature methods

Mittal

Dahiya

2015

Computers & Mathematics with Applications

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Available online xxxx Keywords:Hyperbolic diffusion problem Cubic B-spline functions Modified cubic B-spline differential quadrature method System of ordinary differential equations Runge-Kutta 4th order method a b s t r a c tIn this article, a modified cubic B-spline differential quadrature method (MCB-DQM) is proposed to solve a hyperbolic diffusion problem in which flow motion is affected by both convection and diffusion. One dimensional hyperbolic non-homogeneous heat, wave and telegraph equations are also considered along with two dimensional hyperbolic diffusion problem. The method reduces the hyperbolic problem into a system of nonlinear ordinary differential equations. The system is then solved by the optimal four stage three order strong stability-preserving time stepping Runge-Kutta (SSP-RK43) scheme. The reliability and efficiency of the method has been tested on seven examples. The stability of the method is also discussed and found to be unconditionally stable.

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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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Shock wave simulations using Sinc Differential Quadrature Method

Cited by 114 publications

References 39 publications

Numerical Solutions of Differential Equations Using Modified B-spline Differential Quadrature Method

Numerical Solutions of Differential Equations Using Modified B-spline Differential Quadrature Method

Numerical simulation on hyperbolic diffusion equations using modified cubic B-spline differential quadrature methods

A Novel Approach for Numerical Computation of Fokker-Planck Equation

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