Regarding the group preserving scheme and method of line to the numerical simulations of Klein–Gordon model

In this work a powerful method is presented to solve the Klein–Gordon equation (KGE). Firstly, a discretization is implemented on the original equation. Then a geometric technique is applied to obtain the approximate solutions. Some examples containing one-dimensional and two-dimensional are solved to prove the power and the capability of the offered scheme. Indeed, graphs of the exact solution, numerical solution, absolute error and the contour plot of error are provided successfully.