A new unconditionally stable compact difference scheme of O (τ2+h4)(τ2+h4) for the 1D linear hyperbolic equation

In this paper, we propose a three level compact difference scheme of O(τ2+h4)O(τ2+h4) for the difference solution of one-dimensional second-order non-homogeneous linear hyperbolic equation utt+2αut+β2u=uxx+f(x,t)utt+2αut+β2u=uxx+f(x,t), 0000, where α>β⩾0α>β⩾0. Stability analysis of the method has been carried out. Finally, numerical examples are used to illustrate the efficiency of the new difference scheme.