Numerical schemes for the solution of the telegrapher equation

Abstract The present work deals with the numerical resolution of the telegrapher equation. We present various numerical explicit and implicit schemes for problems defined in one-dimensional domains. In this case, we consider, on one hand, Dirichlet boundary value conditions and in the other hand, the mixed ones. In both cases, we analyze the stability by using the classical Von Neumann method or the matricial one. Moreover, the truncation error of the presented schemes are computed. The cases of two- and three-dimensional cases, is also briefly considered with only the Dirichlet boundary value conditions and in simple geometries. Concerning the implicit schemes, we briefly survey the main classical numerical linear algebra algorithms and we show that they can be applied successfully to the numerical solution of the target problem. We briefly consider the cases where, the coefficients of the problem are not constant and, also, the case where the linear problem is perturbed by a singlevalued or a multivalued diagonal operator. This study is completed by numerical simulations in the case of one-dimensional problems.