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A Galerkin-Type Method to Solve One-Dimensional Telegraph Equation Using Collocation Points in Initial and Boundary Conditions

In this study, a Galerkin-type approach is presented in order to numerically solve one-dimensional hyperbolic telegraph equation. The method includes taking inner product of a set of bivariate 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 bivariate 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 four examples. Lastly, the results obtained from the present scheme are compared with other methods present in the literature.