4.3.0.0.3 RK2:

A time-integrator that advances a field $\Phi$ⁿ at time n , to time n + 1 . For the ODE system

$${\frac{{d \mathbf{\Phi}}}{{d t}}} \Phi$$ (4.5)

it adopts the following algorithm

$$\Phi \Phi \Delta \Phi \Delta$$ =

$$\Phi \Phi {\frac{{\Delta t}}{{2}}} \left(\vphantom{ F(\mathbf{\Phi}^n, n \Delta t) + F(\mathbf{\Phi}^{(1)}, (n+1) \Delta t) }\right. \Phi \Delta \Phi \Delta \left.\vphantom{ F(\mathbf{\Phi}^n, n \Delta t) + F(\mathbf{\Phi}^{(1)}, (n+1) \Delta t) }\right)$$ = (4.6)

Therefore, the integrator has no idea of the dimensionality of space, but makes copious use of the functionality in the FieldVar for the imposition of boundary conditions and ghost-cell updates.