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You might ask yourself whether we can compute the solution backwards
in time. Physically, given the temperature at some time, can we use
this information to construct what the temperature was at earlier
times? (The change in the direction of time can be simulated by
instead merely reversing the sign of in the heat equation.
Such a heat equation with a negative conduction coefficient is called
a backward heat equation.) Although you might think solving backwards
in time is possible, the difficulty is that small scale features of
the temperature distribution in the bar diffuse away very quickly, and
are impossible to reconstruct using a computer with a finite accuracy.
So generally it is not possible to compute the temperature at earlier
times than is given.
Next: The convection equation.
Up: The heat equation.
Previous: About numerical solutions.