An Asymptotic-Numerical Hybrid Method for Solving Singularly Perturbed Linear Delay Differential Equations
In this work, 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 effici...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2017/7269450 |
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| author | Süleyman Cengizci |
| author_facet | Süleyman Cengizci |
| author_sort | Süleyman Cengizci |
| collection | DOAJ |
| description | In this work, 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. |
| format | Article |
| id | doaj-art-cbdb03608e584fd9b5d63104da1055d1 |
| institution | DOAJ |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-cbdb03608e584fd9b5d63104da1055d12025-08-20T03:23:35ZengWileyInternational Journal of Differential Equations1687-96431687-96512017-01-01201710.1155/2017/72694507269450An Asymptotic-Numerical Hybrid Method for Solving Singularly Perturbed Linear Delay Differential EquationsSüleyman Cengizci0Institute of Applied Mathematics, Middle East Technical University, 06800 Ankara, TurkeyIn this work, 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.http://dx.doi.org/10.1155/2017/7269450 |
| spellingShingle | Süleyman Cengizci An Asymptotic-Numerical Hybrid Method for Solving Singularly Perturbed Linear Delay Differential Equations International Journal of Differential Equations |
| title | An Asymptotic-Numerical Hybrid Method for Solving Singularly Perturbed Linear Delay Differential Equations |
| title_full | An Asymptotic-Numerical Hybrid Method for Solving Singularly Perturbed Linear Delay Differential Equations |
| title_fullStr | An Asymptotic-Numerical Hybrid Method for Solving Singularly Perturbed Linear Delay Differential Equations |
| title_full_unstemmed | An Asymptotic-Numerical Hybrid Method for Solving Singularly Perturbed Linear Delay Differential Equations |
| title_short | An Asymptotic-Numerical Hybrid Method for Solving Singularly Perturbed Linear Delay Differential Equations |
| title_sort | asymptotic numerical hybrid method for solving singularly perturbed linear delay differential equations |
| url | http://dx.doi.org/10.1155/2017/7269450 |
| work_keys_str_mv | AT suleymancengizci anasymptoticnumericalhybridmethodforsolvingsingularlyperturbedlineardelaydifferentialequations AT suleymancengizci asymptoticnumericalhybridmethodforsolvingsingularlyperturbedlineardelaydifferentialequations |