Asymptotic Stability of a Finite Difference Scheme for a Wave Equation with Delayed Damping
In this paper, we propose an implicit finite difference scheme for a wave equation with strong damping and a discrete delay term. Although the scheme is implicit, the use of second-order finite difference approximations for the strong damping term in both space and time prevents it from being uncond...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-06-01
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| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/14/7/497 |
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| Summary: | In this paper, we propose an implicit finite difference scheme for a wave equation with strong damping and a discrete delay term. Although the scheme is implicit, the use of second-order finite difference approximations for the strong damping term in both space and time prevents it from being unconditionally stable. A sufficient condition for the asymptotic stability of the scheme is established by applying the Jury stability criterion to show that all roots of the characteristic polynomial associated with the resulting linear recurrence lie strictly inside the unit disk. This stability condition is derived under an appropriate constraint that links the time and space discretization steps with the damping and delay parameters. A numerical example is provided to illustrate the decay behavior of the scheme and confirm the theoretical findings. |
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| ISSN: | 2075-1680 |