Application of a fourth-order compact ADI method to solve a two-dimensional linear hyperbolic equation

Deng, Dingwen; Zhang, Chengjian

doi:10.1080/00207160.2012.713475

Cited by 22 publications

(6 citation statements)

References 27 publications

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“…More important compact ADI schemes with the 4th approximation order, i.e. O(h 4 t + |h| 4 ), for such 2D and 3D equations were constructed and studied, in particular, in [4,5,12,19,24]. For the variable coefficient 2D wave equation, the compact ADI scheme having the approximation order O(h 2 t + |h| 6 ) has recently been constructed in [3], and the 4th order compact ADI-like schemes were proposed and studied in the 2D and 3D cases in [10,13,23].…”

Section: Introductionmentioning

confidence: 99%

On properties of an explicit in time fourth-order vector compact scheme for the multidimensional wave equation

Zlotnik

2021

Preprint

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An initial-boundary value problem for the n-dimensional wave equation is considered. A threelevel explicit in time and conditionally stable 4th-order compact scheme constructed recently for n = 2 and the square mesh is generalized to the case of any n 1 and the rectangular uniform mesh. Another approach to approximate the solution at the first time level (not exploiting high-order derivatives of the initial functions) is suggested. New stability bounds in the mesh energy norms and the discrete energy conservation laws are given, and the 4th order error bound is rigorously proved. Generalizations to the cases of the non-uniform meshes in space and time as well as of the wave equation with variable coefficients are suggested.

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Section: Introductionmentioning

confidence: 99%

On properties of an explicit in time fourth-order vector compact scheme for the multidimensional wave equation

Zlotnik

2021

Preprint

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“…Recent applications are [1], [13], [14], [22], [24], and [28]. A CFD formula linearly couples discrete evaluations of a function and its derivative of certain order at subsequent grid points, and requires solving a banded systems of linear equations (SEL) for the latter values along a whole grid line.…”

Section: Introductionmentioning

confidence: 99%

Alternating direction implicit time integrations for finite difference acoustic wave propagation: Parallelization and convergence

et al. 2020

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“…High order compact finite difference scheme is an efficient way for solving PDEs. In [23][24][25], the high order compact finite difference scheme was constructed for hyperbolic equations subject to homogeneous boundary condition.…”

Section: Introductionmentioning

confidence: 99%

A New Numerical Approximation Method for Two-Dimensional Wave Equation with Neumann Damped Boundary

Liu

Zhang

2020

Complexity

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In this paper, a fully discretized finite difference scheme is derived for two-dimensional wave equation with damped Neumann boundary condition. By discrete energy method, the proposed difference scheme is proven to be of second-order convergence and of unconditional stability with respect to both initial conditions and right-hand term in a proper discretized L2 norm. The theoretical result is verified by a numerical experiment.

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Application of a fourth-order compact ADI method to solve a two-dimensional linear hyperbolic equation

Cited by 22 publications

References 27 publications

On properties of an explicit in time fourth-order vector compact scheme for the multidimensional wave equation

On properties of an explicit in time fourth-order vector compact scheme for the multidimensional wave equation

Alternating direction implicit time integrations for finite difference acoustic wave propagation: Parallelization and convergence

A New Numerical Approximation Method for Two-Dimensional Wave Equation with Neumann Damped Boundary

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