Numerical solution of coupled nonlinear Klein-Gordon equations on unbounded domains

The numerical solution of coupled nonlinear Klein-Gordon equations on unbounded domains is considered by applying the artificial boundary method. Based on the unified approach to overcome the coupled nonlinearity, local artificial boundary conditions are designed on the introduced artificial boundaries. The original problem is reduced to an initial boundary value problem on a bounded domain, which can be efficiently solved by the finite difference method. Some numerical examples are provided to verify the accuracy and effectiveness of the proposed method.