the central equations of the GNOR model, based on Ref. [@MortensenGNOR]. In the GNOR model, also diffusion of the electron gas is taken into consideration. Let the density $n({\mathbf{r}},t)=n_0+n_1({\mathbf{r}},t)$, where the last term is the induced density variation caused by a non-vanishing electric field ${\mathbf{E}}$, which we assume sufficiently small that $n_1\ll n_0$ holds. Instead of , we now consider the linearized convection-diffusion equation [@MortensenGNOR] $$\label{eq:cd}
\partial_t (-e_1) n_1 = D\nabla^2(-e)n_1-\nabla\cdot[(-e)n_0{\mathbf{v}}]=-\nabla\cdot{\mathbf{J}},$$ where $D$ is the diffusion constant for the charge-carrier diffusion. Then the current density is given by Fick’s law $$\label{eq:current}
{\mathbf{J}}= (-e)n_0{\mathbf{v}}-D\nabla(-e)n_1.$$ Multiplying by the charge of the electron $-e$, the equilibrium density $n_0$ and taking the time-derivative we have $$\label{eq:hddv}
m_e(\partial_t+\gamma)\partial_t[(-e)n_0{\mathbf{v}}]=n_0e^2\partial_t{\mathbf{E}}-m_e\beta^2\nabla[\partial_t(-e)n_1].$$ Dividing by $m_e$ and combining with Fick’s law  results in $$\label{eq:hddj}
(\partial_t+\gamma)\{\partial_t{\mathbf{J}}+D\nabla[\partial_t(-e)n_1]\}=\frac{n_0e^2}{m_e}\partial_t{\mathbf{E}}-\beta^2\nabla[\partial_t(-e)n_1].$$ From the convection-diffusion equation , we have $$\label{eq:hdd}
(\partial_t+\gamma)[\partial_t{\mathbf{J}}+D\nabla(\nabla\cdot{\mathbf{J}})]=\frac{n_0e^2}{m_e}\partial_t{\mathbf{E}}-\beta^2\nabla(\nabla\cdot{\mathbf{J}}).$$ Like what we did for , transforming to the frequency domain gives $$\label{eq:gnor}
\omega(\omega+{\mathrm{i}}\gamma){\mathbf{J}}+[\beta^2+D(\gamma-{\mathrm{i}}\omega)]\nabla(\nabla\cdot{\mathbf{J}})={\mathrm{i}}\omega\omega^2_p\varepsilon_0{\mathbf{E}}.$$ The physical predictions obtained by the GNOR and NHD models often differ substantially, as illustrated below. However, from a computational point of view the GNOR model only differs by the replacement $\beta^2\rightarrow\beta^2+D(\gamma-{\mathrm{i}}\omega)$ in the frequency domain, whereby the nonlocal hydrodynamic parameter acquires an often non-negligible imaginary part. In the GNOR model we 