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Determination of an additive time-and space-dependent coefficient in the heat equation

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Figure

Figure 1: The exact (44) and numerical solutions for the temperature u(x, t), with various meshsizes (a) M = N = 10, (b) M = N = 20, and (c) M = N = 40, for the direct problem
Figure 2: The exact and numerical solutions for: (a)M β(t) and (b) ψ(x), various mesh sizes = N ∈ {10, 20, 40}, for the direct problem.
Table 1: The (sizesrmse) given by equations (46) and (47) for β(t) and ψ(x), with various mesh M = N ∈ {10, 20, 40}, for the direct problem.
Figure 3: Objective function (49) for Example 1 with no noise and no regularization.
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