To solve this problem it is enough to changethe Dirichlet boundary
conditions at the right end on the Neumann boundary conditions. This is
what I tried to do in the code. However, quantitative comparison of the
results showed a significant difference in the results. For example, at
the right boundary at t = 5 according to the exact solution u(x=1,t=5)
must have the value 1.1, but Deal.ii gives the value 5941.66.
Could you please help check a code below and point out my mistakes?

You'll have to debug your code yourself, I'm afraid, and in general there is little we can do without having access to the entire code.

That said, the value is *much* too large, of course. Can you check whether the solution grows exponentially with time, or when the solution starts to be so large? My best guess is that the time step may be too large and that you could fix this by choosing a smaller time step.

Best
 W.

------------------------------------------------------------------------
Wolfgang Bangerth               email:            [email protected]
                                www: http://www.math.tamu.edu/~bangerth/

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