广义罗森诺-KdV-RLW方程的两种六阶、L∞收敛且稳定的紧凑差分方案

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2024-11-19 DOI:10.1016/j.cam.2024.116382

Xin Zhang , Yiran Zhang , Qunzhi Jin , Yuanfeng Jin

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引用次数: 0

摘要

本文利用新颖的六阶算子，研究了广义 Rosenau-KdV-RLW 方程的两种六阶紧凑有限差分方案。一个是两级非线性差分方案，另一个是三级线性化差分方案。这两种方案在时间和空间上都分别达到了二阶和六阶精度。所提出的两种方案在离散意义上保留了原始方程的关键特性。为了验证理论结论，我们给出了数值结果，证明了所提出的紧凑方法的效率和可靠性。值得注意的是，所提出的六阶算子可以扩展到其他方程的数值算法中。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Two sixth-order, L∞ convergent, and stable compact difference schemes for the generalized Rosenau-KdV-RLW equation

In this paper, two sixth-order compact finite difference schemes for the generalized Rosenau-KdV-RLW equation are investigated, which utilize novel sixth-order operators. One is a two-level nonlinear difference scheme, while the other is a three-level linearized difference scheme. The schemes both achieve second-order and sixth-order accuracy in time and space, respectively. The proposed two schemes preserve key properties of the original equation in a discrete sense. Numerical results are presented to validate the theoretical findings, demonstrating the efficiency and reliability of the proposed compact approaches. Significantly, the proposed sixth-order operators can be extended to numerical algorithms for other equations.

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.