Analysis of a backward Euler-type scheme for Maxwell’s equations in a Havriliak–Negami dispersive medium

For the Maxwell’s equations in a Havriliak–Negami (H-N) dispersive medium, associated energy dissipation law has not been settled at both continuous level and discrete level. In this paper, we rigorously show that of H-N model can be bounded by initial is well-posed. We analyse backward Euler-type semi-discrete scheme, prove modified decays monotonically time. Such strong stability ensures scheme unconditionally stable. also introduce fast temporal convolution algorithm to alleviate burden history dependence polarisation relation involving singular kernel with Mittag-Leffler function three parameters. provide ample numerical results demonstrate efficiency accuracy full-discrete via spectra-Galerkin method two dimensions. Finally, consider an interesting application recovery complex relative permittivity some related physical quantities.