Coupled Maxwell equations for electromagnetic scattering (Q1918304)

If \(E(t)\) and \(H(t)\) are respectively the electric and magnetic fields at any time, the author suggests that a convenient approximation to solutions of Maxwell's equations in a conducting medium is given by \[ E(t)= \sum^n_{m= 0} E_m,\quad H(t)= \sum^n_{m= 0} H_m, \] where \(E_{n+ 1}= \varepsilon^{- 1} L^{- 1} [\nabla\times H_n- \sigma E_n]\), \(H_{n+ 1}= -\mu^{- 1} L^{- 1} \nabla \times E_n\), \(E_0= E(0)\), \(H_0= H(0)\), and \(L^{- 1}(.)= \int^t_0 (.)dt\).