The operational matrices of two dimensional Bernstein polynomials for solving the hyperbolic partial differential equation with boundary conditions

The wave equations are one of the most important equations in engineering and physics, which are usually formulated as hyperbolic partial differential equations with special boundary conditions. In this paper, a numerical method for solving these equations based on Bernstein polynomials is introduced. The properties of Bernstein polynomial operational matrices turn this differential equation and its boundary conditions into a system of algebraic equations. Some numerical examples illustrate the accuracy, validity, and applicability of the new technique.