Fourth-order compact difference and alternating direction implicit schemes for telegraph equations

In this paper, two- and three-level compact difference and alternating direction implicit schemes are presented for the numerical solutions of one- and two-dimensional linear telegraph equations and telegraph equations with nonlinear forcing term. The stability and error estimates are given. The convergence rates of the present schemes are of order O(τ2+h4)O(τ2+h4). Numerical experiments on model problems show that the present schemes are of high accuracy.