Computing the variable coefficient telegraph equation using a discrete eigenfunctions method

This paper deals with the construction of discrete numerical solutions of mixed problems for the telegraph equation. After discretization, the two-variables partial difference mixed problem is solved by means of a discrete eigenfunctions method that mimics the advantages of the continuous eigenfunction method while eliminating its computational disadvantages. The solution is based on a closed form solution of the inhomogeneous second order difference equation without increasing the problem’s dimension.