An Efficient Compact Difference Scheme for the Symmetric Regularized Long Wave Equation

GAO Jingying; HE Siriguleng; QING Mei; Eerdunbuhe

doi:10.21656/1000-0887.440374

Volume 46 Issue 3

Mar. 2025

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Article Navigation > Applied Mathematics and Mechanics > 2025 > 46(3): 412-424

GAO Jingying, HE Siriguleng, QING Mei, Eerdunbuhe. An Efficient Compact Difference Scheme for the Symmetric Regularized Long Wave Equation[J]. Applied Mathematics and Mechanics, 2025, 46(3): 412-424. doi: 10.21656/1000-0887.440374

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An Efficient Compact Difference Scheme for the Symmetric Regularized Long Wave Equation

doi: 10.21656/1000-0887.440374

School of Mathematics and Big Data, Hohhot Minzu College, Hohhot 010051, P.R.China

Received Date: 2023-12-29
Rev Recd Date: 2024-07-16
Publish Date: 2025-03-01

Abstract

Abstract

A new efficient and compact finite difference scheme was constructed to obtain numerical solutions of the symmetric regularized long wave equation. The classic Crank-Nicolson (C-N) scheme and the extrapolation technique were used for discretization of the 1st-order derivatives in the temporal direction, the 4th-order Padé method and the inverse compact operator were applied for discretization of the 1st-order and 2nd-order derivatives in the spatial direction, respectively. The constructed scheme has the linear, uncoupled, and compact features, greatly enhancing the computational efficiency. Additionally, analyses on conservation laws, a priori estimates, stability and convergence were conducted for the new scheme, to prove the 2nd-order temporal and the 4th-order spatial convergence accuracies. Finally, the theoretical correctness and efficiency of the scheme were verified through a numerical example.
- symmetric regularized long wave equation,
- finite difference,
- efficient,
- compact

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References(22)

References

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