Compact structure-preserving approach to solitary wave in shallow water modeled by the Rosenau-RLW equation

© 2018 Elsevier Inc. 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 develo...

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Main Authors: B. Wongsaijai, T. Mouktonglang, N. Sukantamala, K. Poochinapan
Format: Journal
Published: 2018
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http://cmuir.cmu.ac.th/jspui/handle/6653943832/62930
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Institution: Chiang Mai University
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spelling th-cmuir.6653943832-629302018-12-14T03:41:35Z Compact structure-preserving approach to solitary wave in shallow water modeled by the Rosenau-RLW equation B. Wongsaijai T. Mouktonglang N. Sukantamala K. Poochinapan Mathematics © 2018 Elsevier Inc. 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. 2018-12-14T03:41:35Z 2018-12-14T03:41:35Z 2019-01-01 Journal 00963003 2-s2.0-85052998990 10.1016/j.amc.2018.06.009 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85052998990&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/62930
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
topic Mathematics
spellingShingle Mathematics
B. Wongsaijai
T. Mouktonglang
N. Sukantamala
K. Poochinapan
Compact structure-preserving approach to solitary wave in shallow water modeled by the Rosenau-RLW equation
description © 2018 Elsevier Inc. 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.
format Journal
author B. Wongsaijai
T. Mouktonglang
N. Sukantamala
K. Poochinapan
author_facet B. Wongsaijai
T. Mouktonglang
N. Sukantamala
K. Poochinapan
author_sort B. Wongsaijai
title Compact structure-preserving approach to solitary wave in shallow water modeled by the Rosenau-RLW equation
title_short Compact structure-preserving approach to solitary wave in shallow water modeled by the Rosenau-RLW equation
title_full Compact structure-preserving approach to solitary wave in shallow water modeled by the Rosenau-RLW equation
title_fullStr Compact structure-preserving approach to solitary wave in shallow water modeled by the Rosenau-RLW equation
title_full_unstemmed Compact structure-preserving approach to solitary wave in shallow water modeled by the Rosenau-RLW equation
title_sort compact structure-preserving approach to solitary wave in shallow water modeled by the rosenau-rlw equation
publishDate 2018
url https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85052998990&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/62930
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