 Compact structure-preserving approach to solitary wave in shallow water modeled by the Rosenau-RLW equationB. Wongsaijai, T. Mouktonglang, N. Sukantamala and K. Poochinapan Applied Mathematics and Computation, 2019, vol. 340, issue C, 84-100 Abstract: A mass-preserving scheme, a nonlinear algorithm based on modification of a finite difference method to the Rosenau-RLW equation, is proposed subject to homogeneous boundary conditions. The key feature of the method for improving the accuracy of approximate solutions is to develop a compact higher-order scheme together with an iterative algorithm for solving the nonlinear implicit scheme. The derivatives for space discretization are approximated by using the algorithm dealing with a five-point stencil. In addition, a three-level average difference technique is used to perform time discretization. The conservation of mass and both the existence and uniqueness of the numerical solution are proved. The stability and convergence of the numerical solution with order O(τ4+τ2h2+h4) are also confirmed. For efficiency analysis, numerical results show that the computational efficiency of the compact scheme is much higher than that of non-compact schemes. Moreover, long-time behavior is also used to validate the capability of the present method. Keywords: Solitary wave; Shallow water; Rosenau-RLW equation; Compact finite difference method (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:340:y:2019:i:c:p:84-100 DOI: 10.1016/j.amc.2018.06.009 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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