OICC Press Mathematical Sciences 2251-7456 16 3 (September 2022) 2021 06 02 Numerical solution by quintic B-spline collocation finite element method of generalized Rosenau–Kawahara equation 10.1007/s40096-021-00413-5 EN Sibel Özer Department of Mathematics, Inonu University, Malatya, 44280, TR Journal Article 2021 06 02 Abstract In this study, numerical solution of generalized Rosenau–Kawahara equation with quintic B-spline collocation finite element method has been obtained. First, the generalized Rosenau–Kawahara equation is converted into a coupled differential equation system by the change of variable for the derivative with respect to space variable. Then, the numerical integrations of the resulting system according to time and space were obtained using the Crank–Nicolson-type formulation and quintic B-spline functions, respectively. The obtained numerical scheme has been applied to four model problems. It is seen that the results obtained from the presented scheme are compatible with the analytical solution, the error norms are smaller than those given in the literature, and conservation constants remain virtually unchanged.