Numerical simulation and convergence analysis of a high-order conservative difference scheme for SRLW equation

Hu, Jinsong; Zheng, Kelong; Zheng, Minggang

doi:10.1016/j.apm.2014.04.062

Cited by 19 publications

(30 citation statements)

References 14 publications

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“…The impact on the results of the actual value of a small parameter

normalθ

in a nonlinear term is judiciously evaluated by numerical experiments and show that, for

θ \in (- 1, 0.5)

, the results are correct with the same significant digits as the truncation error. The numerical results of the proposed format are compared with the numerical results of , and the results show that the proposed format has higher error accuracy. Moreover, the present method gives an implicit linear system, which can be easily implemented.…”

Section: Resultsmentioning

confidence: 99%

“…We compute the error at the different times and compare it to the error from methods in to illustrate the accuracy of the scheme. In Tables and , the comparisons of

‖ e ‖_{\infty, h}

by the compact scheme with the Hu et al scheme and the Yimnet et al scheme are shown. From Tables and , we can see that our compact scheme is acceptable.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…From Tables 1 and 2 and Figures 1 and 2, �e n � ∞ ≤ O(τ 2 + h 4 ) is validated. We compute the error at the different times and compare it to the error from methods in [19,20] to illustrate the accuracy of the scheme. In Tables 3 and 4, the comparisons of �e� ∞,h by the compact…”

Section: Comparison Of Errors and Convergencementioning

confidence: 99%

“…In , some conservative difference schemes for SRLW equations were proposed and converges with order

O ({normalτ}^{2} + h^{2})

in the

L^{\infty}

norm for

u

, and in the

L^{2}

norm for

normalρ

. In , have proposed some noncompact finite difference schemes using a five‐point stencil for solving this system, which has the theoretical accuracy of

O ({normalτ}^{2} + h^{4})

. Moreover, Yimnet et al obtained a four‐level average difference scheme.…”

Section: Introductionmentioning

confidence: 99%

“…For example, the accomplishment of a numerical estimation in the long‐time behavior is assured by schemes for the conservation of energy and mass. In , many conservative finite difference schemes were used for various nonlinear wave equations. Recently, there has been growing interest in high‐order compact (HOC) methods for solving partial differential equations (PDEs) .…”

Section: Introductionmentioning

confidence: 99%

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Numerical study of a conservative weighted compact difference scheme for the symmetric regularized long wave equations

2018

Numerical Methods Partial

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In this article, a new weighted and compact conservative difference scheme for the symmetric regularized long wave (SRLW) equations is considered. The new scheme is decoupled and linearized in practical computation, that is, at each time step only two tridiagonal systems of linear algebraic equations need to be solved. It is proved by the discrete energy method that the compact scheme is uniquely solvable, the convergence and stability of the difference scheme are obtained, and its numerical convergence order is O ( normalτ 2 + h 4 ) in the L ∞ ‐norm. Numerical experiment results show that the scheme is efficient and reliable.

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“…The impact on the results of the actual value of a small parameter

normalθ

in a nonlinear term is judiciously evaluated by numerical experiments and show that, for

θ \in (- 1, 0.5)

Section: Resultsmentioning

confidence: 99%

“…We compute the error at the different times and compare it to the error from methods in to illustrate the accuracy of the scheme. In Tables and , the comparisons of

‖ e ‖_{\infty, h}

by the compact scheme with the Hu et al scheme and the Yimnet et al scheme are shown. From Tables and , we can see that our compact scheme is acceptable.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Section: Comparison Of Errors and Convergencementioning

confidence: 99%

“…In , some conservative difference schemes for SRLW equations were proposed and converges with order

O ({normalτ}^{2} + h^{2})

in the

L^{\infty}

norm for

u

, and in the

L^{2}

norm for

normalρ

. In , have proposed some noncompact finite difference schemes using a five‐point stencil for solving this system, which has the theoretical accuracy of

O ({normalτ}^{2} + h^{4})

. Moreover, Yimnet et al obtained a four‐level average difference scheme.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Numerical study of a conservative weighted compact difference scheme for the symmetric regularized long wave equations

2018

Numerical Methods Partial

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Numerical analysis of an uncoupled and linearized compact difference scheme with energy dissipation property for the generalized dissipative symmetric regularized long‐wave equations

Wang

2023

Math Methods in App Sciences

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This paper proposes and analyzes an uncoupled and linearized compact finite difference scheme for the generalized dissipative symmetric regularized long‐wave (GDSRLW) equations. The unique solvability and some a priori estimates of the proposed difference scheme are rigorously proved based on the mathematical induction method. To obtain the ‐norm estimation of numerical solutions, the discrete energy method is used to prove the convergence and stability of the difference scheme. The proposed difference scheme preserves the original energy dissipation property, and the convergence of the scheme is proved to be fourth‐order in space and second‐order in time in the ‐norm for both and . Some numerical experiments are given to verify the theoretical analysis and the reliability of the proposed difference scheme.

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Coupled and decoupled high‐order accurate dissipative finite difference schemes for the dissipative generalized symmetric regularized long wave equations

Wang

Dai

2021

Numerical Methods Partial

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In this paper, two coupled and decoupled dissipative finite difference schemes with high-order accuracy are proposed for solving the dissipative generalized symmetric regularized long wave equations. Dissipation of the discrete energy of scheme with different parameters is discussed. A priori estimate, existence and uniqueness of numerical solutions, convergence with O(𝜏 2 +h 4 ) and stability of the schemes are proved by the discrete energy method. Numerical examples are given to support the theoretical analysis.

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Numerical simulation and convergence analysis of a high-order conservative difference scheme for SRLW equation

Cited by 19 publications

References 14 publications

Numerical study of a conservative weighted compact difference scheme for the symmetric regularized long wave equations

Numerical study of a conservative weighted compact difference scheme for the symmetric regularized long wave equations

Numerical analysis of an uncoupled and linearized compact difference scheme with energy dissipation property for the generalized dissipative symmetric regularized long‐wave equations

Coupled and decoupled high‐order accurate dissipative finite difference schemes for the dissipative generalized symmetric regularized long wave equations

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