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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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