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The finite difference (FD) method is often used when a function
sampled on a homogeneous mesh
a differential equation that can simply be approximated with
finite difference quotients (1.4.2#eq.2).
In explicit schemes, the solution is calculated directly in terms
of known quantities: explicit schemes are usually easy to implement in
a program, but more delicate to execute.
Implicit schemes are more robust at execution, but result in more
complicated codes solving a linear system: this can be slow in 2 or
higher dimensions and is then often advantageous to reconsider a more
general finite elements solution on an inhomogeneous mesh.