A high-order accurate finite difference scheme for the KdV equation with time-periodic boundary forcing

Dai, Weizhong; Usman, Muhammad

doi:10.1016/j.apnum.2020.09.020

Cited by 14 publications

(1 citation statement)

References 37 publications

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“…Recently, Courtès et al [5] designed a convergent finite difference scheme considering a 4-point θ scheme for the dispersive term and demonstrated its first order accuracy. For other finite difference related work involving (1.1), one can refer to [12,21,27,11,23,1,30] and references therein. Apart from the finite difference approaches, there are developments in the direction of Galerkin schemes for (1.1).…”

Section: Introductionmentioning

confidence: 99%

Convergence of a Conservative Crank-Nicolson Finite Difference Scheme for the KDV Equation

DWIVEDI,

Sarkar

2024

Preprint

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In this paper, we study the stability and convergence of a conservative Crank-Nicolson finite difference scheme applied to the Korteweg-De Vries (KdV) equation endowed with initial data. We design a three-point average scheme associated to the convective term and the dispersion term is discretized by certain discrete operators along with the Crank-Nicolson scheme for the temporal discretization to establish that the proposed scheme is L 2 -conservative. The convergence analysis reveals that utilizing inherent Kato’s local smoothing effect, the proposed scheme converges to a classical solution for sufficiently regular initial data u 0 ∈ H 3 ( R ) and to a weak solution in L 2 ( 0 , T ; L loc 2 ( R ) ) for non-smooth initial data u 0 ∈ L 2 ( R ) . Optimal convergence rates in both space and time for the devised scheme are derived. The theoretical results are justified through several numerical illustrations.

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Section: Introductionmentioning

confidence: 99%

Convergence of a Conservative Crank-Nicolson Finite Difference Scheme for the KDV Equation

DWIVEDI,

Sarkar

2024

Preprint

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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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Fully Discrete Finite Difference Schemes for the Fractional Korteweg-de Vries Equation

Dwivedi,

Sarkar

2024

J Sci Comput

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A high-order accurate finite difference scheme for the KdV equation with time-periodic boundary forcing

Cited by 14 publications

References 37 publications

Convergence of a Conservative Crank-Nicolson Finite Difference Scheme for the KDV Equation

Convergence of a Conservative Crank-Nicolson Finite Difference Scheme for the KDV Equation

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

Fully Discrete Finite Difference Schemes for the Fractional Korteweg-de Vries Equation

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