(17) |

(18) | |||

(19) |

after each other. The first equation is dealt with by the Roe solver routine, the second one you will have to write an integration routine for. Since it is an ordinary differential equation, standard methods can be used. Do not use a very fancy method however, realise that both the Roe solver and the splitting are only second order accurate, so it is not necessary to be more accurate than that when solving Eq. (19).

One can show that a more accurate (but perhaps unnecessary) approach
to the splitting is to integrate Eq. 19 over
,
then Eq. 18 over , then Eq. 19 over
again. This is known as *Strang splitting*.