2023
DOI: 10.1002/mma.9099
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Uniform exponential decay of the energy for a fully discrete wave equation with point‐wise dissipation

Abstract: In this paper, the uniform exponential decay of the energy for a fully discretization of the 1-D wave equation has been studied with a punctual interior damping at 𝜉 (𝜉 ∈ (0, 1)). It is known that the usual scheme obtained with a space discretization is not uniformly exponential decaying. In this direction, we have introduced an implicit finite difference scheme that differs from the usual centered one by additional terms of order h 2 and 𝛿t 2 (where h and 𝛿t represent the discretization parameters). In th… Show more

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