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An Asymptotic-Numerical Hybrid Method for Solving Singularly Perturbed Linear Delay Differential Equations
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10.1155-2017-7269450.pdf
Date
2017
Author
Cengizci, Süleyman
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In thiswork, approximations to the solutions of singularly perturbed second-order linear delay differential equations are studied. We firstly use two-term Taylor series expansion for the delayed convection term and obtain a singularly perturbed ordinary differential equation (ODE). Later, an efficient and simple asymptotic method so called Successive Complementary Expansion Method (SCEM) is employed to obtain a uniformly valid approximation to this corresponding singularly perturbed ODE. As the final step, we employ a numerical procedure to solve the resulting equations that come from SCEM procedure. In order to show efficiency of this numerical-asymptotic hybrid method, we compare the results with exact solutions if possible; if not we compare with the results that are obtained by other reported methods.
Subject Keywords
Boundary-value-problems
,
Uniformly valid approximation
,
Finite-difference
,
Small shifts
,
Layer
URI
https://hdl.handle.net/11511/51638
Journal
International Journal of Differential Equations
DOI
https://doi.org/10.1155/2017/7269450
Collections
Graduate School of Applied Mathematics, Article
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S. Cengizci, “An Asymptotic-Numerical Hybrid Method for Solving Singularly Perturbed Linear Delay Differential Equations,”
International Journal of Differential Equations
, pp. 1–8, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/51638.