A differential quadrature algorithm to solve the two dimensional linear hyperbolic telegraph equation with Dirichlet and Neumann boundary conditions

Jiwari, Ram; Pandit, Sapna; Mittal, R. C.

doi:10.1016/j.amc.2012.01.006

Cited by 71 publications

(48 citation statements)

References 26 publications

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“…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. Here, in this article an approach based on modified cubic B-spline functions has been proposed to find the weighting coefficients of differential quadrature method.…”

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

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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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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

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“…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. Here, in this article an approach based on modified cubic B-spline functions has been proposed to find the weighting coefficients of differential quadrature method.…”

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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“…One of the main advantages of meshless methods is that the selection of field nodes could be controlled automatically and adaptively in theory, but for most of existing methods of solving nonlinear PDE, the nodal distribution is preassigned [24,29,[38][39][40][41][42][43]. And it is clear that an adaptive selection of nodes will be more effective and accurate than a preassigned nodal distribution to capture the soliton structure.…”

Section: Introductionmentioning

confidence: 99%

“…In a strong form formulation, it is assumed that the approximate unknown function should have sufficient degree of consistency, so that it is differentiable up to the order of the PDEs, and a series of meshless strong form approaches were presented in Refs. [10,[21][22][23][24][25][26][27][28][29][30]. Unfortunately, a strong form of equation is difficult for practical engineering problems that are usually complex in nature.…”

Section: Introductionmentioning

confidence: 99%

A numerical meshless method of soliton-like structures model via an optimal sampling density based kernel interpolation

Lü

Luo

2015

Computer Physics Communications

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A differential quadrature algorithm to solve the two dimensional linear hyperbolic telegraph equation with Dirichlet and Neumann boundary conditions

Cited by 71 publications

References 26 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 numerical meshless method of soliton-like structures model via an optimal sampling density based kernel interpolation

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