A numerical algorithm for the third-order partial differential equation with time delay

Ashyralyev, Allaberen; Hınçal, Evren; Ibrahim, Suleiman

doi:10.1063/1.5136176

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2020

2024

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Cited by 3 publications

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“…2. The mixed problem for the one-dimensional DPDE with the Dirichlet condition was studied in [41]. The first and second order of accuracy DSs for the numerical solution of this problem were presented.…”

Section: Discussionmentioning

confidence: 99%

On the Absolute Stable Difference Scheme for Third Order Delay Partial Differential Equations

2020

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The initial value problem for the third order delay differential equation in a Hilbert space with an unbounded operator is investigated. The absolute stable three-step difference scheme of a first order of accuracy is constructed and analyzed. This difference scheme is built on the Taylor’s decomposition method on three and two points. The theorem on the stability of the presented difference scheme is proven. In practice, stability estimates for the solutions of three-step difference schemes for different types of delay partial differential equations are obtained. Finally, in order to ensure the coincidence between experimental and theoretical results and to clarify how efficient the proposed scheme is, some numerical experiments are tested.

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Section: Discussionmentioning

confidence: 99%