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Title: An Actuated Computational Method for Treating Parabolic Partial Delay Integro-Differential Equations Constrained by Infinite Boundary
Authors: Kurkcu, Omur Kivanc
Keywords: Error bound estimation
matrix-collocation method
spatial-temporal delays
Issue Date: 2023
Publisher: Springer Basel Ag
Abstract: For the first time via this study, the ultimate effort is inclined to numerically solve one-dimensional parabolic partial integro-differential equations with spatial-temporal delays and infinite boundary using an efficient matrix-collocation method dependent upon the orthoexponential polynomials. The method clearly actuates a novel procedure converting the unknown differential and delay terms into their matrix expansions at the collocation points, and evaluating the integral part bounded by the half-line. The existence of the singular integral part is also validated by the orthoexponential polynomial solution. In addition to these novelties, an error bound estimation is developed via a boundary property of the orthoexponential polynomials. The resulting solutions are improved via the residual error analysis. Some numerical benchmark examples are included to indicate the accuracy and validity of the method, deploying graphical and numerical instruments. It can be noticeable to conclude that the proposed method achieves both drastic and useful approximation for highly stiff problems derived from the aforementioned equations.
ISSN: 1660-5446
Appears in Collections:Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collections
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collections

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