Thai Journal of Mathematics Volume 17 (2019) Number 3 : 789–803 http://thaijmath.in.cmu.ac.th ISSN 1686-0209 Fourth-Order Conservative Algorithm for Nonlinear Wave Propagation: the Rosenau-KdV Equation Rakbhoom Chousurin † , Thanasak Mouktonglang ‡,§ and Phakdi Charoensawan ‡,§, 1 † Graduate’s Degree Program in Applied Mathematics Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand e-mail : caremarpae@hotmail.com ‡ Center of Excellence in Mathematics, CHE Si Ayutthaya, Bangkok 10400, Thailand § Department of Mathematics, Faculty of Science Chiang Mai University, Chiang Mai 50200, Thailand e-mail : mouktonglang.thanasak@gmail.com (T. Mouktonglang) phakdi@hotmail.com (P. Charoensawan) Abstract : In this paper, we introduce a conservative difference method for solving the Rosenau-KdV equation. The existence of the approximate solution from the difference scheme is shown. We also prove the stability and convergence of this scheme. The presented method gives second- and fourth-order accurate in time and space, respectively. Numerical examples demonstrate the theoretical results. Keywords : Rosenau-KdV equation; wave propagation; convergence. 1 Introduction A nonlinear wave phenomenon is one of the important areas of scientific re- search. A category of wave phenomena can be commonly expressed by using 1 Corresponding author. Copyright c  2019 by the Mathematical Association of Thailand. All rights reserved.