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2.5 Implicit Crank-Nicholson
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As mentioned earlier, implicit schemes involve the coupling between
unknowns and require solving a linear system.
This makes the implementation considerably more complicated, so that the
finite element method from sect.3 is often preferable because it
offers additional flexibility for the same programming effort.
Two popular applications below are based on the scheme that has originally
been proposed by Crank and Nicholson: the first deals with diffusion
dominated problems and the second solves the time-dependent Schrödinger
equation from quantum mechanics.
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