Exponential Collocation Method for Solutions of Singularly Perturbed Delay Differential Equations
This paper deals with the singularly perturbed delay differential equations under boundary conditions. A numerical approximation based on the exponential functions is proposed to solve the singularly perturbed delay differential equations. By aid of the collocation points and the matrix operations,...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/493204 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832563973350752256 |
|---|---|
| author | Şuayip Yüzbaşı Mehmet Sezer |
| author_facet | Şuayip Yüzbaşı Mehmet Sezer |
| author_sort | Şuayip Yüzbaşı |
| collection | DOAJ |
| description | This paper deals with the singularly perturbed delay differential equations under boundary conditions. A numerical approximation based on the exponential functions is proposed to solve the singularly perturbed delay differential equations. By aid of the collocation points and the matrix operations, the suggested scheme converts singularly perturbed problem into a matrix equation, and this matrix equation corresponds to a system of linear algebraic equations. Also, an error analysis technique based on the residual function is introduced for the method. Four examples are considered to demonstrate the performance of the proposed scheme, and the results are discussed. |
| format | Article |
| id | doaj-art-2ae546a7399644f99d2bee6a7fcf043a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-2ae546a7399644f99d2bee6a7fcf043a2025-02-03T01:12:10ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/493204493204Exponential Collocation Method for Solutions of Singularly Perturbed Delay Differential EquationsŞuayip Yüzbaşı0Mehmet Sezer1Department of Mathematics, Faculty of Science, Akdeniz University, Antalya 07058, TurkeyDepartment of Mathematics, Faculty of Science, Celal Bayar University, Manisa 45040, TurkeyThis paper deals with the singularly perturbed delay differential equations under boundary conditions. A numerical approximation based on the exponential functions is proposed to solve the singularly perturbed delay differential equations. By aid of the collocation points and the matrix operations, the suggested scheme converts singularly perturbed problem into a matrix equation, and this matrix equation corresponds to a system of linear algebraic equations. Also, an error analysis technique based on the residual function is introduced for the method. Four examples are considered to demonstrate the performance of the proposed scheme, and the results are discussed.http://dx.doi.org/10.1155/2013/493204 |
| spellingShingle | Şuayip Yüzbaşı Mehmet Sezer Exponential Collocation Method for Solutions of Singularly Perturbed Delay Differential Equations Abstract and Applied Analysis |
| title | Exponential Collocation Method for Solutions of Singularly Perturbed Delay Differential Equations |
| title_full | Exponential Collocation Method for Solutions of Singularly Perturbed Delay Differential Equations |
| title_fullStr | Exponential Collocation Method for Solutions of Singularly Perturbed Delay Differential Equations |
| title_full_unstemmed | Exponential Collocation Method for Solutions of Singularly Perturbed Delay Differential Equations |
| title_short | Exponential Collocation Method for Solutions of Singularly Perturbed Delay Differential Equations |
| title_sort | exponential collocation method for solutions of singularly perturbed delay differential equations |
| url | http://dx.doi.org/10.1155/2013/493204 |
| work_keys_str_mv | AT suayipyuzbası exponentialcollocationmethodforsolutionsofsingularlyperturbeddelaydifferentialequations AT mehmetsezer exponentialcollocationmethodforsolutionsofsingularlyperturbeddelaydifferentialequations |