Numerical solution of the Rosenau equation using quintic collocation B-spline method

Abstract

In this paper , the quintic B-spline collocation scheme is employed to approximate numerical solution of the KdV-like Rosenau equation . This scheme is based on the Crank-Nicolson formulation for time integration and quintic B-spline functions for space integration . The unconditional stability of the present method is proved using Von- Neumann approach . Since we do not know the exact solution of the nonlinear KdV-like Rosenau equation , a comparison between the numerical solutions on a coarse mesh and those on a refine mesh is made to show the efficiency of discussed method.