Abstract
In this study, the Rosenau-Korteweg-de Vries-Regular Longwave (Rosenau-KdV-RLW) equation has been converted into a partial differential equation system consisting of two equations using a splitting technique.  Then, numerical solutions for the Rosenau-KdV-RLW equation system have been obtained using separately both cubic and quintic B-spline finite element collocation method.  For the unknowns in those equations, B-spline functions at x-position and Crank-Nicolson type finite difference approaches at time positions are used.  A test problem has been chosen to check the accuracy of the proposed discretized scheme.  The basic conservation properties of the Rosenau-KdV-RLW equation have been shown to be protected by the proposed numerical scheme.  The results are compared with the analytical solution of the problem and the results given in the literature.  For the reliability of the method the error norms L_2 and L_∞ are calculated.  It is seen that the proposed method gives harmonious results with exact solutions.
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