On Tsertsvadzeʹs difference scheme for the Kuramoto-Tsuzuki equation

In this paper, we have proved the second-order convergence in L∞ norm of the Tsertsvadzeʹs difference scheme for the Kuramoto-Tsuzuki equation. The existence, uniqueness and iterative algorithm are also discussed in detail. Furthermore, a L∞ second order convergent linearized difference scheme is given for inhomogeneous equation. All results are obtained without any restrictions on the meshsizes. At last a numerical example is presented.