After that, the system of PDEs is discretized, creating a finite difference equation for each point in their interior. Specific terms are recognized, and the best implemented scheme for these terms dispatched. For example, advection terms are discretized with the upwind scheme. There are also special schemes for the nonlinear Laplacian and spherical Laplacian. See [here for how this term matching occurs](https://github.com/SciML/MethodOfLines.jl/blob/master/src/discretization/generate_finite_difference_rules.jl), note that the order the generated rules are applied is important, with more specific rules applied first to avoid their terms being matched incorrectly by more general rules. The [SymbolicUtils.jl docs](https://symbolicutils.juliasymbolics.org/rewrite/) are a useful companion here. See [here for the practical implementation of the finite difference schemes](https://github.com/SciML/MethodOfLines.jl/blob/master/src/discretization/differential_discretizer.jl).
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