A conservative weighted finite difference scheme for regularized long wave equation

Shao, Xin-Hui; Xue, Guanyu; Li, Changjun

doi:10.1016/j.amc.2013.03.068

Cited by 18 publications

(13 citation statements)

References 17 publications

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“…So, with the steep slope, the rate of the growth undulation is sharp and then decrease slowly. Figure 7 (right) shows the linear behavior in time of the invariants for d = 5, which coincides with the results in (23). The values of the quantities I 1 and I 3 for d = 5 and d = 2 are respectively reported in Table III.…”

Section: A Rlw Equationsupporting

confidence: 83%

“…It is clear that the LEP‐II scheme provides the most accurate solution than the others. To compare the accuracies of solution of the LEP schemes with those of the momentum‐preserving schemes and multisymplecticity‐preserving scheme , we carry out the simulations with

c = 4 / 3

x \in [- 50, 50]

τ = 0.1

, and different spatial steps up to

T = 1

. The results shown in Table indicate that both the LEP‐I and ‐II schemes provide more accurate solutions than the conservative schemes in .…”

Section: Some Numerical Resultsmentioning

confidence: 99%

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Efficient local structure‐preserving schemes for the RLW‐type equation

Cai

Hong

2017

Numerical Methods Partial

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The multisymplectic schemes have been used in numerical simulations for the RLW‐type equation successfully. They well preserve the local geometric property, but not other local conservation laws. In this article, we propose three novel efficient local structure‐preserving schemes for the RLW‐type equation, which preserve the local energy exactly on any time‐space region and can produce richer information of the original problem. The schemes will be mass‐ and energy‐preserving as the equation is imposed on appropriate boundary conditions. Numerical experiments are presented to verify the efficiency and invariant‐preserving property of the schemes. Comparisons with the existing nonconservative schemes are made to show the behavior of the energy affects the behavior of the solution.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1678–1691, 2017

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Section: A Rlw Equationsupporting

confidence: 83%

c = 4 / 3

x \in [- 50, 50]

τ = 0.1

, and different spatial steps up to

T = 1

. The results shown in Table indicate that both the LEP‐I and ‐II schemes provide more accurate solutions than the conservative schemes in .…”

Section: Some Numerical Resultsmentioning

confidence: 99%

Efficient local structure‐preserving schemes for the RLW‐type equation

Cai

Hong

2017

Numerical Methods Partial

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“…Lemma 2.2 (Shao et al 2013) For any mesh function U ∈ Z 0 h , there exist two positive constants C 1 and C 2 such that…”

Section: )mentioning

confidence: 99%

A new conservative finite difference scheme for the generalized Rosenau–KdV–RLW equation

Dai

2020

Comp. Appl. Math.

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In this paper, a new conservative fourth-order finite difference scheme is proposed for solving the generalized Rosenau-KdV-RLW equation. The solvability, convergence, and conservation of the numerical solution are discussed by the discrete energy method. The scheme is convergent of O(τ 2 + h 4) and unconditionally stable. Several numerical experiment results show that the proposed scheme is efficient and reliable.

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“…It can also be used to describe wave propagation and spread interaction (Cui and Mao 2007). There are a lot of theoretical and numerical studies on the well-known KdV equation and its variational forms (Bahadir 2005;Ma et al 2011;Dutykh et al 2013;Shao et al 2013;García-Alvarado and Omel'yanov 2014;Wang et al 2014;Vaneeva et al 2014;Wang and Dai 2018). However, in the study of the dynamics of compact discrete systems, the well-known KdV equation cannot describe well the wave-wave and wave-wall interactions (Hu and Wang 2013).…”

Section: Introductionmentioning

confidence: 99%

A new implicit energy conservative difference scheme with fourth-order accuracy for the generalized Rosenau–Kawahara-RLW equation

Dai

2018

Comp. Appl. Math.

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In the present work, a new implicit fourth-order energy conservative finite difference scheme is proposed for solving the generalized Rosenau-Kawahara-RLW equation. We first design two high-order operators to approximate the third-and fifth-order derivatives in the generalized equation, respectively. Then, the generalized Rosenau-Kawahara-RLW equation is discreted by a three-level implicit finite difference technique in time, and a fourth-order accurate in space. Furthermore, we prove that the new scheme is energy conserved, unconditionally stable, and convergent with O(τ 2 + h 4). Finally, two numerical experiments are carried out to show that the present scheme is efficient, reliable, high-order accurate, and can be used to study the solitary wave at long time.

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A conservative weighted finite difference scheme for regularized long wave equation

Cited by 18 publications

References 17 publications

Efficient local structure‐preserving schemes for the RLW‐type equation

Efficient local structure‐preserving schemes for the RLW‐type equation

A new conservative finite difference scheme for the generalized Rosenau–KdV–RLW equation

A new implicit energy conservative difference scheme with fourth-order accuracy for the generalized Rosenau–Kawahara-RLW equation

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