Compact difference schemes for solving telegraphic equations with Neumann boundary conditions

In this paper, based on the generalized trapezoidal formula, a family of unconditionally stable compact difference schemes including a parameter θ,θ∈[0,1] are discussed for the numerical solution of one-dimensional telegraphic equations with Neumann boundary conditions. In general, the accuracy of these schemes is second-order in time and third-order in time and third in space. Interestingly, there exist a method of the family which is third-order in time. We also consider extensions of the presented difference schemes to a nonlinear problem. Numerical results demonstrate the superiority of our new schemes.