407 | | [[latex(e^{n+1}_i-e^{n}_i = \frac{\Delta t}{\Delta x} \left ( f \left ( e^n_i \right ) + g \left ( e^n_i,E^*,\nabla E^* \right ) \right ) + \left ( \left ( \bar{\psi} - 1 \right ) \phi \right ) e^n_i + \psi \phi e^{n+1}_i) ]] |

408 | | |

409 | | which can be solved for [[latex(e^{n+1} = \frac{1}{1-\psi \phi} \left ( \left ( \bar{\psi} - 1 \right ) \phi e^n_i + f \left ( e^n_i \right ) + g \left ( e^n_i,E^*,\nabla E^* \right ) \right ) )]] |

| 407 | [[latex(e^{n+1}_i-e^{n}_i = \frac{\Delta t}{\Delta x} \left ( f \left ( e^n_i \right ) + g \left ( e^n_i,E^*,\nabla E^* \right ) \right ) + \left ( \left ( \bar{\psi} - 1 \right ) \phi \right ) e^n_i + \psi \phi e^{n+1}_i) ]] |

| 408 | |

| 409 | which can be solved for |

| 410 | [[latex(e^{n+1}_i = \frac{1}{1 - \psi \phi} \left ( \left ( \bar{\psi} - 1 \right ) \phi e^n_i + f \left ( e^n_i \right ) + g \left ( e^n_i,E^*,\nabla E^* \right ) \right ) )]] |