# Solution of the Blatter-Pattyn model

The final form of the equations we'd like to solve is:

Again, note that for the *x* equation we've moved all the terms containing gradients in *v* to the right-hand side (RHS).

We've set it up this way in order to solve the equations using an **operator splitting** approach; for the *x* equation, we treat *v* as known (where we take the values of *v* from the previous iteration) and solve for *u*, and vice versa when we solve they *y* equation for *v*. The "splitting" refers to the fact that we are breaking the multi-dimensional divergence operation into multiple steps. Rather than solving one big matrix equation for *u* and *v* simultaneously we solve two smaller matrix equations in sequence with one of the unknowns treated as a known "source" term.

... unsure on how much more detail to go into on this ...

- symmetry in the equations means that the same subroutines can be used for the discretization of both the *u* and *v* equations. For example,