Application of quintic B-splines collocation method for solving inverse Rosenau equation with Dirichlet’s boundary conditions

In this paper, we discuss a numerical method for solving an inverse Rosenau equation with Dirichlet’s boundary conditions. The approach used is based on collocation of a quintic B-spline over finite elements so that we have continuity of dependent variable and it first four derivatives throughout the solution range. We apply quintic B-spline for spatial variable and derivatives which produce an ill-posed system. We solve this system using Tikhonov regularization method. The accuracy of the proposed method is demonstrated by applying it on a test problem. Figures and comparisons have been presented for clarity. The main advantage of the resulting scheme is that the algorithm is very simple, so it is very easy to implement.