A Galerkin-like scheme to solve two-dimensional telegraph equation using collocation points in initial and boundary conditions

In this study, a Galerkin-like approach is presented in order to numerically solve two-dimensional hyperbolic telegraph equation. The method includes converting the equation to a finite number of algebraic equations by means of taking inner product of a set of three-variable monomials with a vector obtained from the equation in question. The initial and boundary conditions are also taken into account by a suitable utilization of collocation points. The resulting linear system is then solved, yielding a polynomial as the approximate solution. Additionally, the technique of residual correction, which aims to increase the accuracy of the approximate solution, is discussed briefly. The method and the residual correction technique are illustrated with two example problems. In order to evaluate the efficiency of the proposed scheme, the numerical results of both examples are compared with several methods.