Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.11851/1674
Title: Comparison of Nonlocal Operators Utilizing Perturbation Analysis
Authors: Aksoylu, Burak
Çeliker, Fatih
29230
Keywords: Kernel Function
 Transition Point
 Classical Operator
 Perturbation Expansion
 Boundary Condition
Issue Date: 2016
Publisher: Springer Verlag
Source: Aksoylu, B., & Celiker, F. (2016). Comparison of nonlocal operators utilizing perturbation analysis. In Numerical Mathematics and Advanced Applications ENUMATH 2015 (pp. 589-606). Springer, Cham.
Abstract: We present a comparative study of integral operators used in nonlocal problems. The size of nonlocality is determined by the parameter ?. The authors recently discovered a way to incorporate local boundary conditions into nonlocal problems. We construct two nonlocal operators which satisfy local homogeneous Neumann boundary conditions. We compare the bulk and boundary behaviors of these two to the operator that enforces nonlocal boundary conditions. We construct approximations to each operator using perturbation expansions in the form of Taylor polynomials by consistently keeping the size of expansion neighborhood equal to ?. In the bulk, we show that one of these two operators exhibits similar behavior with the operator that enforces nonlocal boundary conditions.
URI: https://doi.org/10.1007/978-3-319-39929-4_57
https://hdl.handle.net/20.500.11851/1674
ISBN: 978-331939927-0
ISSN: 1439-7358
Appears in Collections:Matematik Bölümü / Department of Mathematics
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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