  We develop numerical methods for solving the spin-2 Gross-Pitaevskii
equation. The basis of our work is a two-way splitting of this evolution
equation that leads to two exactly solvable subsystems. Utilizing second-order
and fourth-order composition schemes we realize two fully symplectic
integration algorithms, the first such algorithms for evolving spin-2
condensates. We demonstrate the accuracy of these algorithms against other
methods on application to an exact continuous wave solution that we derive.
