A new linear difference scheme for generalized Rosenau-Kawahara equation (Q1721148)

Summary: We introduce in this paper a new technique, a semiexplicit linearized Crank-Nicolson finite difference method, for solving the generalized Rosenau-Kawahara equation. We first prove the second-order convergence in \(L_{\infty}\)-norm of the difference scheme by an induction argument and the discrete energy method, and then we obtain the prior estimate in \(L_{\infty}\)-norm of the numerical solutions. Moreover, the existence, uniqueness, and satiability of the numerical solution are also shown. Finally, numerical examples show that the new scheme is more efficient in terms of not only accuracy but also CPU time in implementation.