On the Stability of the Time Delay Telegraph Equation with Neumann Condition

In this paper, we consider the initial-boundary value problem for time delay telegraph equation with Neumann condition. Stability estimates for the solution of this problem are obtained. A first order of accuracy difference scheme is constructed. Stability estimates for the solution of this difference scheme are established. As a test problem, one-dimensional time delay telegraph equation with Neumann condition is considered. Numerical results are given. © 2021, Springer Nature Switzerland AG.