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In this paper, a collocation method based on Bessel functions of first kind is applied to solve the one-dimensional wave equation subject to the Dirichlet, Neumann boundary, and the integral conditions. Firstly, the matrix forms of these functions with two variables are constructed. Secondly, the matrix forms of the solution form and its partial derivatives are organized and thus each terms of wave equation are written in matrix form. Similarly, the matrix forms of the Dirichlet, Neumann boundary, and the integral conditions of the problem are constructed. By using the collocation points, these matrix equations and matrix operations, the wave problem is reduced to a system of linear algebraic equations. Finally, the solutions of this system determine the coefficients of the assume approximate solution in Bessel series form. An error analysis technique is presented for the method. To demonstrate the validity and applicability of the technique, some numerical examples are solved. The method is easy to implement and produces accurate results. Also, the results of the method are compared with the results of previous methods in literature.

wave equation, boundary value problem, nonlocal integral condition, collocation points, collocation method, Bessel function.