We provide a numerical method in this study to solve the one-dimensional
nonlinear Klein-Gorden problem. We provide a detailed description of the
mathematical formulation process. The technique is based on nonstandard finite
differences and is explicit at three levels. The step sizes' denominator function is
nonlinear. We have provided a stability study of the approach and shown its
unconditional stability when applied to the one-dimensional nonlinear Klein-Gorden
problem. We use the suggested strategy to two cases to demonstrate its utility