High-order compact difference scheme for the regularized long wave equation

Lin, Jianguo, Xie, Zhihua ORCID: https://orcid.org/0000-0002-5180-8427 and Zhou, Juntao 2007. High-order compact difference scheme for the regularized long wave equation. Communications in Numerical Methods in Engineering 23 (2) , pp. 135-156. 10.1002/cnm.892

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Abstract

A numerical simulation of the regularized long wave (RLW) equation is obtained using a high-order compact difference method, based on the fourth-order compact difference scheme in space and the fourth-order Runge–Kutta method in time integration. The method is tested on the problems of propagation of a solitary wave, interaction of two positive solitary waves, interaction of a positive and a negative solitary wave, the evaluation of Maxwellian pulse into stable solitary waves, the development of an undular bore and the solitary waves induced by boundary motion. The three invariants of the motion are calculated to determine the conservation properties of the algorithm. L2 and L∞ error norms are used to measure differences between the exact and numerical solutions. The results obtained by proposed method are compared with those of other recently published methods and shown to be more accurate and efficient.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Engineering
Subjects:	T Technology > TJ Mechanical engineering and machinery
Publisher:	John Wiley & Sons
ISSN:	1069-8299
Last Modified:	02 Nov 2022 10:10
URI:	https://orca.cardiff.ac.uk/id/eprint/97700

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