Time exponential splitting technique for the Klein-Gordon equation with Hagstrom-Warburton high-order absorbing boundary conditions

Abstract

Klein–Gordon equations on an unbounded domain are considered in one dimensional and two dimensional cases. Numerical computation is reduced to a finite domain by using the Hagstrom–Warburton (H-W) high-order absorbing boundary conditions (ABCs). Time integration is made by means of exponential splitting schemes that are efficient and easy to implement. In this way, it is possible to achieve a negligible error due to the time integration and to study the behavior of the absorption error. Numerical experiments displaying the accuracy of the numerical solution for the two dimensional case are provided. The influence of the dispersion coefficient on the error is also studied.