Application of Quintic B-splines Collocation Method on Some Rosenau Type Nonlinear Higher Order Evolution Equations

In this work, we discuss a collocation method for solving some Rosenau type non-linear higher order evolution equations with Dirichlet’s boundary conditions. The approach used, is based on collocation of a 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 SSPRK3 scheme. This method needs less storage space that causes to less accumulation of numerical errors. The numerical approximate solutions to Rosenau type non-linear evolution equations have been computed without transforming the equations and without using the linearization. This method is tested on four test problems where one example is with the variable coefficients. Easy and economical implementation is the strength of this method.