A collocation approach for solving two-dimensional second-order linear hyperbolic equations

In this study, a collocation approach is introduced to solve second-order two-dimensional hyperbolic telegraph equation under the initial and boundary conditions. The method is based on the Bessel functions of the first kind, matrix operations and collocation points. The method is constructed in four steps for the considered problem. In first step we construct the fundamental relations for the solution method. By using the collocation points and matrix operations, second step gives the constructing of the main matrix equation. In third step, matrix forms are created for the initial and boundary conditions. We compute the approximate solutions by combining second and third steps. Algorithm of the proposed method is given. Later, error estimation technique is presented and the approximate solutions are improved. Numerical applications are included to demonstrate the validity and applicability of the presented method.