An unconditionally stable fourth-order method for telegraph equation based on Hermite interpolation

There have been many approaches to solve telegraph equations numerically in literature. However, very few are two-level difference schemes in solving telegraph equations with Dirichlet boundary conditions. In this paper, based on cubic Hermite interpolation, a two-level method is presented for the numerical solutions of one-dimensional telegraph equations. The accuracy of the present scheme is of order O(k4+h4)O(k4+h4). It is proved that the scheme is unconditionally stable. Numerical results are given to illustrate the efficiency of our method.