general Rosenau-RLW Equation , quintic B-splines basis functions , SSP-RK54 scheme , Thomas algorithm"/>, Open Access Library" />
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Numerical solution of General Rosenau-RLW Equation using Quintic B-splines Collocation MethodKeywords: general Rosenau-RLW Equation &searchField=keyword">"">general Rosenau-RLW Equation , quintic B-splines basis functions , SSP-RK54 scheme ,&searchField=keyword"> Thomas algorithm"/> Abstract: 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.
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