A Lie-group Approach for Solving Backward Two-dimensional Nonlinear Klein-gordon Equation

In this paper, the backward two-dimensional nonlinear Klein-Gordon equation is solved by using a Lie-group approach. Because the solution does not continuously depend on the presented data, the inverse problem is famous for seriously ill-posed. A numerical example of the backward nonlinear Klein-Gordon equation demonstrates that this method is applicable, and the computational cost is quite cheap. Although the recovery of a presently wave is from the final time and under a large noise imposed on the final time data, this algorithm still works effectively and accurately. These numerical results are rather important in the computations of backward nonlinear Klein-Gordon equation.