Many fields of physics and technology use hyperbolic partial differential equations pde with initial conditions as models. Recently, significant effort has been invested in investigating these equations, and they have attracted the curiosity of many mathematicians. In this paper, the finite difference method is used to provide the solution to the one-dimensional hyperbolic problem. The wave equation with the first dimension in space and time is taken as the boundary condition. The numerical results obtained from the examples of the Finite Differences Method formulated are compared with an analytical solution showing good results.

Keywords : Hyperbolic Partial Differential Equation, Finite Difference, Wave Equation, Implicit Scheme, Explicit Difference Method.