Split Local Artificial Boundary Conditions for the Two-Dimensional Sine-Gordon Equation on R^(2)

In this paper the numerical solution of the two-dimensional sine-Gordon equation is studied.Split local artificial boundary conditions are obtained by the operator splitting method.Then the original problem is reduced to an initial boundary value problem on a bounded computational domain,which can be solved by the finite differencemethod.Several numerical examples are provided to demonstrate the effectiveness and accuracy of the proposed method,and some interesting propagation and collision behaviors of the solitary wave solutions are observed.