Numerical Integration of a Class of Singularly Perturbed Delay Differential Equations with Small Shift
We have presented a numerical integration method to solve a class of singularly perturbed delay differential equations with small shift. First, we have replaced the second-order singularly perturbed delay differential equation by an asymptotically equivalent first-order delay differential equation....
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2012/572723 |
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| author | Gemechis File Y. N. Reddy |
| author_facet | Gemechis File Y. N. Reddy |
| author_sort | Gemechis File |
| collection | DOAJ |
| description | We have presented a numerical integration method to solve a class of singularly perturbed delay differential equations with small shift. First, we have replaced the second-order singularly perturbed delay differential equation by an asymptotically equivalent first-order delay differential equation. Then, Simpson’s rule and linear interpolation are employed to get the three-term recurrence relation which is solved easily by discrete invariant imbedding algorithm. The method is demonstrated by implementing it on several linear and nonlinear model examples by taking various values for the delay parameter and the perturbation parameter . |
| format | Article |
| id | doaj-art-42aa5b294c324b37b0eb152bc5a77000 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-42aa5b294c324b37b0eb152bc5a770002025-02-03T05:48:08ZengWileyInternational Journal of Differential Equations1687-96431687-96512012-01-01201210.1155/2012/572723572723Numerical Integration of a Class of Singularly Perturbed Delay Differential Equations with Small ShiftGemechis File0Y. N. Reddy1Department of Mathematics, National Institute of Technology, Warangal 506 004, IndiaDepartment of Mathematics, National Institute of Technology, Warangal 506 004, IndiaWe have presented a numerical integration method to solve a class of singularly perturbed delay differential equations with small shift. First, we have replaced the second-order singularly perturbed delay differential equation by an asymptotically equivalent first-order delay differential equation. Then, Simpson’s rule and linear interpolation are employed to get the three-term recurrence relation which is solved easily by discrete invariant imbedding algorithm. The method is demonstrated by implementing it on several linear and nonlinear model examples by taking various values for the delay parameter and the perturbation parameter .http://dx.doi.org/10.1155/2012/572723 |
| spellingShingle | Gemechis File Y. N. Reddy Numerical Integration of a Class of Singularly Perturbed Delay Differential Equations with Small Shift International Journal of Differential Equations |
| title | Numerical Integration of a Class of Singularly Perturbed Delay Differential Equations with Small Shift |
| title_full | Numerical Integration of a Class of Singularly Perturbed Delay Differential Equations with Small Shift |
| title_fullStr | Numerical Integration of a Class of Singularly Perturbed Delay Differential Equations with Small Shift |
| title_full_unstemmed | Numerical Integration of a Class of Singularly Perturbed Delay Differential Equations with Small Shift |
| title_short | Numerical Integration of a Class of Singularly Perturbed Delay Differential Equations with Small Shift |
| title_sort | numerical integration of a class of singularly perturbed delay differential equations with small shift |
| url | http://dx.doi.org/10.1155/2012/572723 |
| work_keys_str_mv | AT gemechisfile numericalintegrationofaclassofsingularlyperturbeddelaydifferentialequationswithsmallshift AT ynreddy numericalintegrationofaclassofsingularlyperturbeddelaydifferentialequationswithsmallshift |