Modal Hermite spectral collocation method for solving multi-dimensional hyperbolic telegraph equations

The present research is contemplated proposing a numerical solution of multi-dimensional hyperbolic telegraph equations with appropriate initial time and boundary space conditions. The truncated Hermite series with unknown coefficients are used for approximating the solution in both of the spatial and temporal variables. The basic idea for discretizing the considered one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) telegraph equations is based on the collocation method together with the Hermite operational matrices of derivatives. The resulted systems of linear algebraic equations are solved by some efficient methods such as LU factorization. The solution of the algebraic system contains the coefficients of the truncated Hermite series. Numerical experiments are provided to illustrate the accuracy and efficiency of the presented numerical scheme. Comparisons of numerical results associated to the proposed method with some of the existing numerical methods confirm that the method is accurate and fast experimentally.