An efficient fourth-order low dispersive finite difference scheme for a 2-D acoustic wave equation

Das, Sambit; Liao, Wenyuan; Gupta, Aditya

doi:10.1016/j.cam.2013.09.006

Cited by 26 publications

(18 citation statements)

References 34 publications

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“…Recently, Das [5] developed a low dispersive finite difference method for two-dimensional a coustic wave equation using Padé approximation, we will discuss this method in detail.…”

Section: Higher Order Compact Alternating Direction Scheme For the Wamentioning

confidence: 99%

“…However, the scheme suffers from a moderate numerical dispersion [5]. Therefore, we modify the scheme by substituting one of the spacial grids (in x-direction) in Equation (30) by non-compact one in Equation (8) to obtain a hybrid scheme.…”

Section: Hybrid Schemementioning

confidence: 99%

“…Therefore, in this paper, firstly, we discussed a conventional higher order finite difference schemes. Then we discussed another higher order finite difference scheme developed by Das [5] and Liao [6]. We also discussed the dispersion properties of these methods by comparing with a conventional higher order finite difference scheme.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Comparison of Finite Difference Schemes for the Wave Equation Based on Dispersion

Abdulkadir¹

2015

JAMP

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Finite difference techniques are widely used for the numerical simulation of time-dependent partial differential equations. In order to get better accuracy at low computational cost, researchers have attempted to develop higher order methods by improving other lower order methods. However, these types of methods usually suffer from a high degree of numerical dispersion. In this paper, we review three higher order finite difference methods, higher order compact (HOC), compact Padé based (CPD) and non-compact Padé based (NCPD) schemes for the acoustic wave equation. We present the stability analysis of the three schemes and derive dispersion characteristics for these schemes. The effects of Courant Friedrichs Lewy (CFL) number, propagation angle and number of cells per wavelength on dispersion are studied.

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“…Recently, Das [5] developed a low dispersive finite difference method for two-dimensional a coustic wave equation using Padé approximation, we will discuss this method in detail.…”

Section: Higher Order Compact Alternating Direction Scheme For the Wamentioning

confidence: 99%

Section: Hybrid Schemementioning

confidence: 99%

See 1 more Smart Citation

Comparison of Finite Difference Schemes for the Wave Equation Based on Dispersion

Abdulkadir¹

2015

JAMP

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“…In effect the integral can be evaluated and with y r 1 and y r replacing y(y r 1 ) and y(y r ), (1.1) becomes y r 1 = y r + h f r + (9) where s p 1 is the remainder term and it is estimated by integrating Newton forward interpolation formula for x = x 0 + uh , we have the following.…”

Section: A the Adams Extrapolation Methodsmentioning

confidence: 99%

Finite Difference Method for Solving the Initial Value Ordinary Differential Equations (ODE)

Ahmed¹

2018

IJRASET

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Many engineering applications can be modeled as differential equations (DE). No doubt it is very important for scientists and engineers know to solve differential equations, either ordinary differential equations (ODE), or partial differential equations (PDE) using numerical methods. Initial value ordinary differential equations arise in various fields such as physics and Engineering. This paper shows the method how to solve the initial value ordinary differential equation on some interval by using finite difference method in a very accurate manner with the formulation of error estimation.

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“…The conventional finite difference scheme (FDS) works efficiently for solving the acoustic wave problems [1][2][3]. However, the FDS is an explicit time-marching algorithm, which means its time step should be limited by the CourantFriedrichs-Levy (CFL) condition.…”

Section: Introductionmentioning

confidence: 99%

New unconditionally stable scheme for solving two-dimensional acoustic wave problems

Zhang

Miao

2016

Acoust. Sci. & Tech.

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An efficient fourth-order low dispersive finite difference scheme for a 2-D acoustic wave equation

Cited by 26 publications

References 34 publications

Comparison of Finite Difference Schemes for the Wave Equation Based on Dispersion

Comparison of Finite Difference Schemes for the Wave Equation Based on Dispersion

Finite Difference Method for Solving the Initial Value Ordinary Differential Equations (ODE)

New unconditionally stable scheme for solving two-dimensional acoustic wave problems

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