<b>A Numerical Study of Initial and Boundary Conditions Problem for Wave Equation Using the Operational Matrices</b>

In this paper, orthogonal polynomials and their operational matrices will be utilized to address the initial and boundary value problems of the one-dimensional wave problem, where the domain of the space variable is bounded, which covers a variety of scientific and engineering operations. Six types of orthogonal polynomials, Include instead of such as the Genocchi, Bernoulli, Legendre, Boubaker, Chebyshev and Standard polynomials. The linear problem with its initial and boundary conditions are transformed to a linear algebraic equations, which can then be solved by utilizing to get an approximate solution for this problem. Some test problems related to the one-dimensional wave equation with different conditions are discussed and solved to show how reliable and efficient the proposed methods. The error norm and the mean square error , were computed; these are presented through analytical tables and graphics showing the rapid convergence for these methods.