Numerical solution of singularly perturbed delay differential equations with layer behavior
We present a numerical method to solve boundary value problems (BVPs) for singularly perturbed differential-difference equations with negative shift. In recent papers, the term negative shift has been used for delay. The Bezier curves method can solve boundary value problems for singularly perturbed...
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| Format: | Article |
| Language: | English |
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Hindawi Publishing Corporation
2014
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| Online Access: | http://psasir.upm.edu.my/id/eprint/34686/ http://psasir.upm.edu.my/id/eprint/34686/1/Numerical%20Solution%20of%20Singularly%20Perturbed%20Delay%20Differential.pdf |
| _version_ | 1848847843134013440 |
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| author | Ghomanjani, Fateme Kilicman, Adem Ghassabzade, Fahimeh Akhavan |
| author_facet | Ghomanjani, Fateme Kilicman, Adem Ghassabzade, Fahimeh Akhavan |
| author_sort | Ghomanjani, Fateme |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | We present a numerical method to solve boundary value problems (BVPs) for singularly perturbed differential-difference equations with negative shift. In recent papers, the term negative shift has been used for delay. The Bezier curves method can solve boundary value problems for singularly perturbed differential-difference equations. The approximation process is done in two steps. First we divide the time interval, into subintervals; second we approximate the trajectory and control functions in each subinterval by Bezier curves. We have chosen the Bezier curves as piecewise polynomials of degree and determined Bezier curves on any subinterval by control points. The proposed method is simple and computationally advantageous. Several numerical examples are solved using the presented method; we compared the computed result with exact solution and plotted the graphs of the solution of the problems. |
| first_indexed | 2025-11-15T09:25:02Z |
| format | Article |
| id | upm-34686 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:25:02Z |
| publishDate | 2014 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-346862017-10-19T08:01:33Z http://psasir.upm.edu.my/id/eprint/34686/ Numerical solution of singularly perturbed delay differential equations with layer behavior Ghomanjani, Fateme Kilicman, Adem Ghassabzade, Fahimeh Akhavan We present a numerical method to solve boundary value problems (BVPs) for singularly perturbed differential-difference equations with negative shift. In recent papers, the term negative shift has been used for delay. The Bezier curves method can solve boundary value problems for singularly perturbed differential-difference equations. The approximation process is done in two steps. First we divide the time interval, into subintervals; second we approximate the trajectory and control functions in each subinterval by Bezier curves. We have chosen the Bezier curves as piecewise polynomials of degree and determined Bezier curves on any subinterval by control points. The proposed method is simple and computationally advantageous. Several numerical examples are solved using the presented method; we compared the computed result with exact solution and plotted the graphs of the solution of the problems. Hindawi Publishing Corporation 2014 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/34686/1/Numerical%20Solution%20of%20Singularly%20Perturbed%20Delay%20Differential.pdf Ghomanjani, Fateme and Kilicman, Adem and Ghassabzade, Fahimeh Akhavan (2014) Numerical solution of singularly perturbed delay differential equations with layer behavior. Abstract and Applied Analysis, 2014. art. no. 731057. pp. 1-4. ISSN 1085-3375; ESSN: 1687-0409 http://www.hindawi.com/journals/aaa/2014/731057/abs/ 10.1155/2014/731057 |
| spellingShingle | Ghomanjani, Fateme Kilicman, Adem Ghassabzade, Fahimeh Akhavan Numerical solution of singularly perturbed delay differential equations with layer behavior |
| title | Numerical solution of singularly perturbed delay differential equations with layer behavior |
| title_full | Numerical solution of singularly perturbed delay differential equations with layer behavior |
| title_fullStr | Numerical solution of singularly perturbed delay differential equations with layer behavior |
| title_full_unstemmed | Numerical solution of singularly perturbed delay differential equations with layer behavior |
| title_short | Numerical solution of singularly perturbed delay differential equations with layer behavior |
| title_sort | numerical solution of singularly perturbed delay differential equations with layer behavior |
| url | http://psasir.upm.edu.my/id/eprint/34686/ http://psasir.upm.edu.my/id/eprint/34686/ http://psasir.upm.edu.my/id/eprint/34686/ http://psasir.upm.edu.my/id/eprint/34686/1/Numerical%20Solution%20of%20Singularly%20Perturbed%20Delay%20Differential.pdf |