In this paper, we demonstrate a modified scheme for solving the nonlinear KleinGordon
equation of PDE hyperbolic types. The Klein-Gordon equation is a relativistic
wave equation version of the Schrodinger equation, which is widely used in quantum
mechanics. Additionally, the nonstandard finite difference scheme has been used
extensively to solve differential equations and we have constructed a modified scheme
based on the nonstandard finite difference scheme associated with harmonic mean
averaging for solving the nonlinear inhomogeneous Klein-Gordon equation where the
denominator is replaced by an unusual function. The numerical results obtained have
been compared and showed to have a good agreement with results attained using the
standard finite difference (CTCS) procedure, which provided that the proposed scheme
is reliable. Numerical experiments are tested to validate the accuracy level of the
scheme with the analytical results.