%0 Journal Article
%T Numerical solution of General Rosenau-RLW Equation using Quintic B-splines Collocation Method
%A R.C. Mittal
%A R.K. Jain
%J Communications in Numerical Analysis
%D 2012
%I International scientific publication and consulting services (ISPACS)
%R 10.5899/2012/cna-00129
%X In this paper a numerical method is proposed to approximate the solution of the nonlinear general Rosenau-RLW Equation. The method is based on collocation of quintic B-splines over finite elements so that we have continuity of the dependent variable and its first four derivatives throughout the solution range. We apply quintic B-splines for spatial variable and derivatives which produce a system of first order ordinary differential equations. We solve this system by using SSP-RK54 scheme. This method needs less storage space that causes to less accumulation of numerical errors. The numerical approximate solutions to the nonlinear general Rosenau-RLW Equation have been computed without transforming the equation and without using the linearization. Illustrative example is included for different value of $p=2,3$ and $6,$ to demonstrate the validity and applicability of the technique. Easy and economical implementation is the strength of this method.
%K "">general Rosenau-RLW Equation
%K quintic B-splines basis functions
%K SSP-RK54 scheme
%K Thomas algorithm"/>
%U http://www.ispacs.com/journals/cna/2012/cna-00129/article.pdf