An Asymptotic-Numerical Hybrid Method for Solving Singularly Perturbed Linear Delay Differential Equations

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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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Citation Formats

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.