A Comparison of Finite Difference Methods for a One-Dimensional Hyperbolic Equation with Nonlocal Boundary Conditions

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.