Stability of a Second Order of Accuracy Difference Scheme for Hyperbolic Equation in a Hilbert Space

Allaberen Ashyralyev and Mehmet Emir Koksal

Discrete Dynamics in Nature and Society, 2007, vol. 2007, 1-25

Abstract:

The initial-value problem for hyperbolic equation d 2 u ( t ) / d t 2 + A ( t ) u ( t ) = f ( t ) ( 0 ≤ t ≤ T ) , u ( 0 ) = ϕ , u ′ ( 0 ) = ψ in a Hilbert space H with the self-adjoint positive definite operators A ( t ) is considered. The second order of accuracy difference scheme for the approximately solving this initial-value problem is presented. The stability estimates for the solution of this difference scheme are established.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:057491

DOI: 10.1155/2007/57491

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